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ADOLPHE QUETELET 9?/ 

STATISTICIAN 



BY 

FRANK H. HANKINS, A. B. 

Sometime University Fellow in Statistics 



SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS 

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY 

IN THE 

Faculty of Political Science 
Columbia University 



1908 



PREFATORY NOTE 



It is not presumed that the dissertation here presented 
will add much to the knowledge of Quetelet possessed 
by those who have read rather extensively in statistical 
literature. But it is hoped that the increasing number 
of those who are becoming interested in Quetelet and 
his work may find these pages useful. The first two 
chapters give brief sketches of the man, his work and 
his place in the history of statistics. The last three 
chapters present what are believed to be the most im- 
portant of Ouetelet's statistical principles. These in- 
clude the conception of the Average Man as a type, the 
significance for social science of the regularities found in 
the moral actions of man, and the theoretical basis of the 
distribution of group phenomena about their type. 

Grateful acknowledgment should here be made to 
Professor Henry L. Moore for directing me to this 
stimulating subject, and for continued helpfulness in its 
pursuit. 

447] 5 



CONTENTS 

CHAPTER I 
Biographical Sketch 

PAGE 

Parentage — Youthful literary activity — At the University of Ghent; 
the influence of Gamier — Called to the Athenaeum at Brussels — 
Contributions to mathematics — Educational activity at Brussels ; 
his elementary treatises and characteristics as a teacher — Found- 
ing of the Brussels Observatory; sojourn in Paris — Travels in 
Germany, Italy and Sicily — Research work at the Observatory — 
Studies in meteorology and terrestrial physics — His activity in 
connection with V Acaditnie royale de Belgique — Activity as an 
official statistician — Founding of the Commission centrale de 
statistique, of the Statistical Society of London and of the Inter- 
national Statistical Congress — Stroke of apoplexy in 1855 — Mem- 
ber of many learned societies — His personality — Home life — The 
Brussels statue 9 

CHAPTER II 

QUETELET IN THE HlSTORY OF STATISTICS 

Two lines of development in statistical literature — One of these, 
the German University ' '' Statistic ,'' " traced through the writings 
of Muenster, Conring, Achenwall, Von Schlozer and Busching — 
The growth of official statistics and the gradual modification of 
the university discipline — Quetelet's contribution to this change 
-—A second line of statistical development traced through the 
works of Graunt, Petty and others of the School of Political 
Arithmetic, Derham, Siissmilch, and the first formulators of 
mortality tables — The influence of Malthus, Laplace, and espe- 
cially of J. B. Fourier — Quetelet's contribution to this line of 
development, treated under (I) population statistics, (II) moral 
statistics; (III) technique and (IV) application of the normal law of 
error to the physical measurements of men — Summary .... 36 

CHAPTER III 

The Average Man 

Importance of this concept in Quetelet's writings — Survey of its 
development— Its generalization in Du Systeme social — Studies 
to determine the qualities of the average man — Role of the aver- 
age man in various sciences — Objections: the average man cannot 
be constructed as a composite being — The average as the type of 
449] 7 



CONTENTS [450 



PAGE 

perfection — Distinction of results obtained in some of Quetelet's 
studies — The average man as a biological type — The permanence 
of the type — Quetelet's approach to the doctrine of selection by 
environment 62 

CHAPTER IV 

Moral Statistics 
Introductory— Definition — Quetelet's principal works on moral sta- 
tistics and his emphasis upon statistical regularities — His explana- 
tion of these regularities — The viewpoint of science and its bearing 
upon the doctrine of free will and upon the explanation of statis- 
tical regularities — Explanation of the fluctuations in the numbers 
from year to year — And of the variations about an average — 
Because of the way in which they are formed, the regularities 
exert no compulsion over the individual — Significance of the reg- 
ularities for the doctrine of free will — Bearing of statistical inquiry 
on this doctrine — The statistical regularities and social laws — The 
difficulty of establishing quantitative relations between social 
events and their conditions — The effect of the dynamic character 
of social life upon statistical regularities and their laws — Two basic 
principles of method in moral statistics — And their importance 
for the quantitative study of social phenomena 83 

CHAPTER V 

Statistical Method 

The basis of statistical method found in the variability of organic 
and social phenomena about type forms — The probability of an 
event when all its chances are known — Inductions from exper- 
ience when the number of chances is unknown — The distribution 
of chances when their number is small— Agreement between 
theory and experience tested — The distribution of chances when 
their number is very large — Quetelet's scale of possibility and 
precision — The derivation of this scale explained — The curve rep- 
resenting the distribution of chances when their number reaches 
the conceptual limit — Theory provides for extremely improbable 
combinations, but such are not met with in experience — Quetelet's 
distinction of "means properly so called" from "arithmetic 
means " — The theory of the distribution of chances related to the 
theory of the distribution of errors of measurement and to the 
distribution of biological measurements— Description of the ap- 
plication of Quetelet's scale to a statistical problem — The probable 
error — The normal curve only one of many possible forms — The 
significance of narrowing limits of deviation — Quetelet's classifi- 
cation of causes — Constant causes not revealed by statistical in- 
quiry — Variable causes — Kinds of accidental causes — Causes clas- 
sified as general and minute — Causes studied by correlation . . . 106 



CHAPTER I 

BIOGRAPHICAL SKETCH 

It might be set down as a rule of mental conduct that, 
when we become interested in the achievements of a 
great man, we desire a more intimate acquaintance with 
his personality and with the routine of his daily life. 
The deeds of statesmen and warriors are readily appre- 
ciated by the generality of men. This is due, not only 
to their conspicuousness and to the glamour and fascina- 
tion attending those who achieve notable success in the 
world of affairs, but to the immediate responsiveness of 
human emotions to the heroic. But not infrequently 
does it happen that many years are required for the most 
important contributions to knowledge to become the 
possession of an extended and appreciative group of 
initiated disciples. Herein is found the reason for this 
brief sketch of Adolphe Quetelet. 1 Not that his scientific 
achievements have been passed by with little or no com- 
ment, but that there is to-day a rapidly widening group 

x Quetelet's name is sometimes accented — Quetelet. There is, how- 
ever, abundant reason for omitting the accent. In the Nouveau Mim- 
oires, the Bulletins and the Annuaire of the Brussels Academy, in the 
Annales and the Annuaire of the Brussels Observatory, and in a num- 
ber of his works brought out at Brussels, the name is uniformly unac- 
cented. When it is recalled that Quetelet was Secretary of the Academy 
for forty years and Director of the Observatory for even a longer term, 
it seems certain that he himself did not accent his name. Moreover in 
places where he has signed his name it is not accented. The accented 
spellings seem to be due to Paris publishers. 

45i] 9 



IO ADOLPHE QUETELET AS STATISTICIAN [452 

of scholars who appreciate the distinctive merit of his 
development of statistical methods of research. It is 
believed that such will be interested in a brief account of 
the man himself. J 

Born on the twenty- second of February, 1796, in the 
ancient and historic town of Ghent, Quetelet grew up 
there amid the stirring scenes which marked the fall of 
the old regime and the rise of the empire of the brilliant 
and ambitious Napoleon. Little is known of his parents. 
No mention is anywhere made of his mother except that 
her maiden name was Anne-Frangoise Vandevelde. His 
father, Frangois-Augustin-Jacques-Henri Quetelet, is 
known to have been born at Ham, in Picardy, in 1756. 
Being of a somewhat adventurous spirit, Frangois crossed 
the English Channel at an early age and is said to have 
become an English citizen. He soon became secretary 
to a Scotch nobleman, with whom he spent several years 
traveling on the Continent and sojourning in Italy. He 
then settled permanently at Ghent, about 1787. Here 
he was at length elevated to the position of a municipal 
officer, in which capacity he rendered valuable and well- 

1 The chief source for this sketch is the ' ' Essai sur la vie et les ouv- 
rages de Quetelet," by Edward Mailly, one of Quetelet's students and 
his assistant for thirty-seven years, in the Annuaire de V acadimie 
royale des sciences, des lettres et des beaux-arts de Belgique (Brussels, 
1875), vol. xli, pp. 109-297. In addition should be mentioned the fol- 
lowing: (1) Naum Reichesberg, " Der beriihmte Statistiker, Adolphe 
Quetelet, sein Leben und sein Wirken," Zeitschrift fur schweizerische 
Statistik (Berne, 1893), Jahrg. xxxii, pp. 418-460; (2) the " Discours " 
pronounced at Quetelet's funeral, Bulletins de V acadhnie royale des 
sciences, des lettres et des beaux-arts de Belgique (Brussels, 1874), 
Second Series, vol. xxxvii, pp. 244-206; (3) Mailly, "Notice sur 
Adolphe Quetelet," ibid., vol. xxxviii, pp. 816-844; (4) Wolowski, 
" Eloge de Quetelet," Journal de la sociiti de statistique de Paris 
(1874), vol. xv, pp. 118-126. Other less important references will be 
found in the notes. 



4 ^3] BIOGRAPHICAL SKETCH IX 

esteemed services. He died in 1803, when Adolphe was 
but a boy of seven. 

It was thus that, upon his graduation from the Lyceum 
at Ghent, young Quetelet was compelled, at the age of 
seventeen, to turn his talents to good account. He 
spent the next year as teacher of mathematics in a 
private school at Audenaerde. x On his nineteenth birth- 
day he was chosen instructor in mathematics at the 
newly organized college in his native city. 

The time between his election and the opening of the 
University in October, 181 7, seems to have been spent 
largely in literary composition. In collaboration with 
G. Dandelin, a former student at the Lyceum, he prepared 
the libretto for an opera "en un acte, en prose et a grand 
spectacle," entitled Jean Second ou Charles Quint dans 
les murs de Gand. This was successfully presented at 
Ghent, and led to the partial construction of two more 
dramas by the same authors. Quetelet published quite 
a number of poems, 2 and until the age of thirty he con- 
tinued to exercise his poetical talents as pastime and 
relief from his scientific studies. His poems were of a 
serious tone, but were well received by both public and 
critics. We may mention here an Essai sur la romance, 
which Quetelet brought out in 1823. In this, from a 
survey of romance among different peoples, he found the 
origin of romance in the days of chivalry. This essay, 
together with translations, in prose and in verse, of Ger- 
man, English, Italian and Spanish romances, shows 
Quetelet's wide acquaintance at that early age with the 

x One of his students here was M. Liedts, who afterwards, as minister 
of the interior, authorized the Commission centrale de la statistique. 

2 Chiefly in the Annates belgiques and Etudes et tecons francaises de 
littirature et de morale. Mailly, Essai, pp. 114-131, quotes at length 
from these poems. 



12 ADOLPHE QUETELET AS STATISTICIAN [454 

various European literatures. Mailly, who must be 
viewed as a friendly critic, believes the Essai sur la 
romance and many of the poems deserving of republi- 
cation. 

During the three years of his service at the College of 
Ghent the most important influence brought to bear 
upon him was that of Jean Guillaume Gamier, 1 professor 
of astronomy and higher mathematics. This expert 
mathematician and refined scholar was called from Paris 
to the University of Ghent by the King of the Low 
Countries in 181 7. His influence over Quetelet's eager, 
youthful spirit was quite decisive. Quetelet says of him, 

Little by little his conversation, always instructive and ani- 
mated, gave a special direction to my tastes, which would 
have led me by preference towards letters. I resolved to 
complete my scientific studies and followed the courses in 
advanced mathematics given by M. Gamier. It was at the 
same time agreed by us that, in order to relieve him in his 
work, I should give some of the other courses with which he 
was charged. I thus found myself his pupil and his colleague. 2 

The aspiring dramatist soon found a favorite occupation 
in the reading of Pascal. 

Quetelet was the first to receive the degree of doctor 
of science from the new university. His dissertation was 
an original contribution of much importance to the 

1 1 766- 1 840. He was examiner at l'Ecole polytechnique, 1795-1800; 
adjunct professor with Lagrange at the same place, 1800-1802; one of 
Poisson's instructors and an intimate of J. B. Fourier. See Nouvelle bio- 
graphie ge'ne'rale (Paris, 1858), vol. xix, also " Notice sur J. G. Gamier," 
by Quetelet, in the Annuaire de Vacadimie royale de Bruxelles (1841), 
vol. 7; and sketch by Quetelet in Sciences mathimatiques et physiques 
au commencement du xixe Steele (Brussels, 1867). 

2 " Notice sur J. G. Gamier," Annuaire de Vacad. roy. de Brux. 
(1841), vol. vii, pp. 200-201. 



45 5] BIOGRAPHICAL SKETCH l ^ 

theory of conic sections : it demonstrated two new prop- 
ositions, one of which developed the properties of a new 
curve, the "focale." 1 In October of this same year 
(1819) he was called to the chair of elementary mathe- 
matics in the Athenaeum at Brussels. Repairing thither 
at once, he was soon in the midst of a learned circle of 
Belgian and French scholars. Among the former may 
be mentioned the old Commandeur de Nieuport, the only 
Belgian scientist then known abroad, and the Baron de 
Reiffenberg. The French savants were refugees enjoying 
the hospitality of the tolerant Pays-Bas. Quetelet's inti- 
macy with them, no doubt, helped to fix his political 
views and, in particular, to accentuate his leanings toward 
liberalism. They were a distinguished company, includ- 
ing such men as the poet Arnault, the artist David, the 
naturalist and traveler Bory de Saint-Vincent and the 
statesman and jurist Merlin de Douai. 

In February, 1820, Quetelet was elected to member- 
ship in the Acadkmie royale des sciences et belles-lettres de 
Bruxelles. The meetings of the Academy, at this time, 
were attended by scarce half a dozen Belgian scholars; 2 
interest in it had almost ceased. Quetelet was soon to be- 
come its moving spirit, to arouse it to renewed activity 
and to make it the inspiration of a new intellectual 
awakening throughout Belgium. His first year in the 

1 The discovery of this curve was hailed as a brilliant achievement by 
his contemporaries. From Reichesberg's essay " Der beriihmte Statis- 
tiker, etc." p. 422, we learn that Raoul, a colleague of Garnier's and 
like him a Parisian and a mathematician, compared this discovery to 
that of Pascal's cycloid, saying that this alone sufficed to place Quete- 
let's name alongside that of the great geometrician. See also Mailly, 
Essai, pp. 115 and 150. 

"Among these were the pharmacist Kickx, the chemist Van Mons, 
and Quetelet's teacher and friend, Gamier, "who strongly urged the 
election of his favorite pupil." Mailly, Essai, p. 135. 



I4 ADOLPHE QUETELET AS STATISTICIAN [456 

Academy was marked by the presentation of two mathe- 
matical memoirs, the second of which, Nouvelle theorie 
des sections coniques considZrees dans le solide, brought 
him much honor. 

During the next nine years, or until 1829, Quetelet 
devoted much attention to mathematics. Physics also 
interested him at this time. 1 His memoirs on these sub- 
jects, published in the Nouveau mkmoires of the Brussels 
Academy, and the Correspondance were both numerous 
and meritorious. 2 " The mere enumeration of his con- 
tributions to pure and mixed mathematics would occupy 
a very large space, and from their intrinsic merit, patient 
and conscientious research and earnest regard for truth, 
would alone have secured him a foremost place among 
the distinguished and scientific men of the present 
century." 3 

During this period appeared the first volumes of the 
Correspondance mathfonatique et physique, 4 with Quet- 
elet and Gamier as joint editors. Beginning with the 
third volume Quetelet alone was editor. Leading mathe- 
maticians and scientists of all Europe, and particularly of 
England, France, Germany and Holland, were con- 
tributors. 5 In this manner Quetelet came into touch 

1 For the flattering reception given one of his memoirs on caustics, 
see Revue encyclopidique, Sept., 1825, vol. xxvii, pp. 794-795. 

2 A general survey of them is given by Mailly, Essai, pp. 131-154. 
3 F. J. Mouat, "Monsieur Quetelet," Journal of the Statistical 

Society of London (1875), vol. xxxvii, p. 114. 

4 Eleven vols.: vols, i and ii at Ghent, the others at Brussels. Vols. 
i-vi, 1825-1830; vols, vii-viii (not located); vols, ix-x-xi, 1837, 1838, 
1839- 

6 Among these were Herschel, Babbage, Wheatstone, Whewell, 
Chasles, Villerme, Ampere, Bouvard, Hachette, Gautier, Gauss, Hans- 
teen, Olbers, De la Rive, Wartmann, Encke, Brandes and Hansen. 
Quetelet has given an account of the Correspondance in his Premier 
siecle de I'acadimie royale de Bruxelles (Brussels, 1872), pp. 36, et seq. 



4 57] BIOGRAPHICAL SKETCH 1 c ) 

with the foremost scholars of his time. The Correspond- 
ance covered every branch of mathematics, as well as 
mechanics, astronomy, physics, meteorology and statis- 
tics. 1 The character of the contributions made this 
journal, for a time, the foremost of its kind in Europe. 2 
Its place was gradually taken by numerous publications 
at home and abroad covering the special fields more in- 
tensively. 

But the chief work of Quetelet during these first years 
at Brussels was educational. We have seen that he came 
to the city in 1820 as professor of elementary mathe- 
matics at the Athenaeum. Four years later he succeeded 
M. Thiry in the chair of higher mathematics in this insti- 
tution, 3 and at the same time began giving popular 
courses in geometry, probabilities, 4 physics and astronomy 
at the Museum, Brussels. The success of these popular 
lectures was so marked that, after two years, the Musee 
des sciences et des lettres was organized, by royal decree, 
on the basis of a plan drawn up by Quetelet. In this 
institution he began giving a course on the history of 

Numerous references in these volumes show Quetelet's early famil- 
iarity with past and current statistical development. As an instance of 
the influence of Jean-Baptiste Fourier, we find in a note, vol. ii, p. 177, 
one of Quetelet's frequent references to Fourier's statement that, " Sta- 
tistics will make progress only as it is retained in the hands of those 
versed in higher mathematics." The first six volumes only (I have 
not seen volumes vii and viii) have statistical articles from Quetelet. 

2 Von John, Geschichte der Statistik (Stuttgart, 1884), p. 334. 

3 Meanwhile he had spent three momentous months in Paris, where 
he met Laplace and others, who profoundly influenced his thought. 
See p. 20, infra. 

4 His first course of instruction in probabilities was given in the 
scholastic year 1824-5 at the Athenaeum; this was the year immediately 
following his sojourn in Paris; the next year (1825-6) he gave an intro- 
ductory course at the Museum. 



l6 ADOLPHE QUETELET AS STATISTICIAN [458 

the sciences. x The following very characteristic state- 
ment, which he often referred to afterwards, was made 
at the opening 1 of this course : 

The more advanced the sciences have become, the more they 
have tended to enter the domain of mathematics, which is a 
sort of center towards which they converge. We can judge 
of the perfection to which a science has come by the facility, 
more or less great, with which it may be approached by calcu- 
lation. 2 

He continued his courses on physics and astronomy at 
the Athenaeum until 1828, when he resigned on account 
of his appointment as astronomer at the observatory. 
But his lectures at the Musee des sciences et des lettres* 
were maintained until the absorption of the Musee by the 
University libi'e in 1834. But he was not allowed to re- 
main long free from professional duties. Two years 
later (1836) he was made professor of astronomy and 
geodesy at the newly erected Ecole militaire at Brussels. 

For his courses at the Mnske he prepared a number of 
elementary treatises which, on account of their clearness 
and exactness, obtained well-merited popularity. The 
first of these, Astro7iomie elhnentaire* was soon followed 

1 This course bore fruit in the publication by him of " Apergude l'etat 
actuel des sciences mathematiques, chez les Beiges," prepared at the 
request of the British Association and published in Report of the British 
Association for the Advancement of Science, vol. v (1835), PP- 35~o6 
and in Correspondance , vol. ix, pp. 1-47; Histoire des sciences mathe- 
matiques et physiques chez les Beiges (Brussels, 1864), and Sciences 
mathematiques et physiques chez les Beiges, au commencement du xix* 
siecle (Brussels, 1866). 

2 Mailly, Essai, p. 159; found also in "Conclusions" of Instruc- 
tions populaires sur le calcul des probabilitis, p. 230. 

"These lectures after 1828 were in astronomy and physics. 

4 Paris, 1826. 



4 ^ 9 ] BIOGRAPHICAL SKETCH jy 

by the TraitS populaire d' astronomies a work of unusual 
merit. It was often reprinted in France and Belgium 
and was translated into several languages. Houzeau 2 
says it was of almost epoch-making importance for the 
spread of the knowledge of astronomy; for, in addition 
to the wide circle of general readers whom it reached, it 
opened the way for popular instruction in the science of 
astronomy. It attained the distinction of being placed 
on the Index librorum prohibitorum by the Catholic 
Church, a fact which hastened and augmented its wide 
influence. About the same time he published his Posi- 
tions de physique ou rksumk d?un cours de physique gkne- 
rale, 3 which was translated into English by Robert Wal- 
lace. 4 The translator says in his preface, "No other 
work in the English language contains such an extensive 
and succinct account of the different branches of physics 
or exhibits such a general knowledge of the whole field 
in so small a compass." 

Among these treatises, besides the De la chaleur, 5 
was the Instructions populaires sur le calcul des proba- 
bility? which, Quetelet says, is "a resume of lectures 
given at the Musee as an introduction to my courses in 
physics and astronomy." 7 It bears on the title-page the 
significant aphorism Mundum numeri regunt. We meet 
in the preface several distinctly typical thoughts. Thus, 

1 Paris, 1827. 2 Reichesberg, " Der beriihmte Statistiker," p. 433. 
3 Three volumes, Paris, 1826. 

4 Facts, Laws and Phenomena of Natural Philosophy, or a Summary 
of a Course in General Physics (Glasgow, 1835). 

5 Brussels (?), 1832. 

6 Brussels, 1828, 236pp. English translation by R. Beamish, London, 
1839. 

7 Preface, p. 1. These courses and this book are of later date than his 
trip to Paris from Dec, 1823, to Feb., 1824. See p. 19, et seq. infra. 



1$ ADOLPHE QUETELET AS STATISTICIAN [ 4 6o 

he says, " It has seemed to me that the theory {calcul) 
of probabilities ought to serve as the basis for the study 
of all the sciences, and particularly of the sciences of 
observation." " Since absolute certainty is impossible, 
and we can speak only of the probability of the fulfill- 
ment of a scientific expectation, a study of this theory 
should be a part of every man's education." The book 
is intended for the general reader, and the only prere- 
quisite is a knowledge of the rules of arithmetic. In a 
most perspicuous manner he expounds the fundamental 
propositions of probabilities, Bernoulli's principle of 
agreement between experience and calculation, precision, 
the principle of least squares, the construction of a mor- 
tality table for a stationary population, and the calcula- 
tion of probable and of average life. We cannot forbear 
another quotation : 

Chance, that mysterious, much abused word, should be con- 
sidered only a veil for our ignorance ; it is a phantom which 
exercises the most absolute empire over the common mind, 
accustomed to consider events only as isolated, but which is 
reduced to naught before the philosopher, whose eye embraces 
a long series of events and whose penetration is not led astray 
by variations, which disappear when he gives himself suffi- 
cient perspective to seize the laws of nature. 1 

As a teacher and lecturer Quetelet was very successful. 
He was considerate and amiable, free from pedantry and 
conceit, and " endowed with a true talent for exposi- 
tion." 2 His courses at the Museum attracted a great 
number of auditors from all ranks of society. Several 
of his pupils at the Athenaeum afterwards became distin- 

1 " Conclusion," p. 230; see also p. 8. 
'Mailly, Essai, p. 156. 



4 6i] BIOGRAPHICAL SKETCH T g 

guished. Joseph Plateau, probably the most eminent 
of these, in dedicating to Quetelet his greatest work, 
Statique experimentale, etc., says : ] 

Vous, qui avez ete 1' un des actifs promoteurs de la regeneration 
intellectuelle de la Belgique, et dont les travaux ont tant 
contribue a l'illustration de ce pays ; vous, qui avez guide mes 
premiers pas dans la carriere des sciences, et qui m' avez 
appris, par votre example, a exciter chez les jeunes gens 
l'amour des recherches ; vous, enfm, qui n'avez cesse d'etre 
pour moi un ami devoue, etc. 

Quetelet is said to have taken an almost paternal 
interest in those of his students who showed special ap- 
titude. He entertained them and opened to them freely 
the rich treasures of his own learning. 2 

During these years of educational activity, an import- 
ant series of events had taken place. Soon after his 
election to the Academy (1820) Quetelet began arousing 
interest in favor of an astronomical observatory. He 
made friends for the project on every hand, secured 
resolutions from the learned societies of Belgium and 
personally won the support of the minister of public in- 
struction, M. Falck. Quetelet himself, having no ex- 
perience with the methods and instruments of practical 
astronomy, was sent to Paris in December, 1823, at the 
expense of the state. He was kindly received at the 
Paris observatory by Arago and Bouvard, the latter of 
whom took special interest in instructing him in the 
knowledge of practical astronomy. 3 

1 Bulletins de I'acad., 2nd series, vol. xxxvii, pp. 253-254, note. 

2 Wolowski, " Eloge de Quetelet," Journal de la sociUi de statistique 
de Paris, vol. xv, p. 122. 

3 For Quetelet's very interesting account of his introduction at the 
observatory at Paris, see " Notice biographique de M. Bouvard," An- 
nuaire of the Brussels Academy (1844), vol. x, pp. 112-113. 



20 ADOLPHE QUETELET AS STATISTICIAN [462 

Bouvard also introduced him to an inner circle of 
friends. Among these were Laplace, Poisson, Alexander 
von Humboldt and Fresnel. It is probable that Quetelet 
at this time formed the acquaintance of Fourier, from 
whom he received some instruction. 1 During his three 
months' 2 study in Paris, doubtless the most significant 
influence on the direction and character of his thought 
was that exerted by the immortal Laplace. Under this 
great mathematician, Quetelet received instruction in 
the theory of probabilities. 3 This course must have ex- 
erted a profound influence on Quetelet's scientific and 
philosophical views. The emphasis which Quetelet laid 
upon the principles of probabilities in his courses at the 
Museum during the years immediately following this 
sojourn in Paris has already been noted. 4 Quetelet's 

*In the Physique sociale (Paris, 1869), vol. ii, notes, p. 446, Quetelet 
says, " During a temporary sojourn at Paris, about a half century ago, 
I had the honor of the kindly friendship of M. Bouvard, who was 
pleased to present me to the illustrious author of the MScanique cileste, 
of which he was the collaborator for a part of the calculations and ob- 
servations. I had the good fortune then of being able to profit by the 
counsel of this great geometrician and to win the friendship of several 
of the most distinguished scholars of France, who ordinarily grouped 
themselves about him. Later Jean-Bapt. Fourier, . . . was pleased 
also to express to me sentiments of kindness ... I had the good fortune 
of enjoying the lessons of these two great masters and I still remember 
with gratitude the encouragement which they were pleased to give me." 

2 Von John, Geschichte der Statistik, p. 233, says two years, but this is 
undoubtedly wrong. Quetelet himself says, " I arrived at Paris towards 
the end of 1823" and "I returned to Belgium in 1824," in sketch of 
Bouvard, Sciences mathimatiques et physiques au commencement du 
xix e siicle, pp. 611-614; Mailly, Essai, p. 172, says that Quetelet re- 
turned to Brussels at the beginning of 1824, and that on the first of 
March he addressed the Academy on the establishment of an obser- 
vatory. 

'See Reichesberg, " Der beruhmte Statistiker," p. 450. 

4 Pp. 15 and 17, supra. 



4 6 3 ] BIOGRAPHICAL SKETCH 2 I 

writings previous to this time, show none of that em- 
phasis on the importance of probabilities in scientific 
researches, which from this time on becomes more and 
more prominent. It would seem, therefore, that this 
contact with Laplace, and with others holding like views, 
implanted in Quetelet's mind the germs of those thoughts 
which afterwards developed into his conception of the 
social system and his methods of investigating its laws. 

After his return to Brussels, the project of an observa- 
tory was advanced, but with discouraging slowness. In 
1827 Quetelet was charged by the King with making the 
first purchase of instruments. In company with his long- 
time friend, Dandelin, he repaired to London. After 
attending to business matters, he spent a couple of 
months in visiting the universities, observatories and 
learned societies of England, Scotland and Ireland. 1 The 
following January he was named astronomer of the Royal 
Observatory at Brussels. However, delays in construc- 
tion, due to differences between the city and national 
governments as to financial support and to the revolution 
of 1830, prevented his occupying the Observatory until 
1832. 

Meanwhile he traveled. From July to October, 1829, 
accompanied by his accomplished wife, 2 he made a tour 
through Holland and Germany. He visited numerous 
astronomers and men of science, inspected the chief 
observatories and made himself familiar with the state of 
astronomical science in Germany. One of the most 
memorable incidents of this eventful journey was Quet- 
elet's visit with the great Goethe at Weimar. Here he 

1 " Description des plusieurs observatoires d'Angleterre," Corres- 
pondance, vols, iv and v. 

2 He had been married in 1825 to the daughter of the French physician 
and refugee, M. Curtet, who was also a niece of the chemist Van Mons. 



22 ADOLPHE QUETELET AS STATISTICIAN [464 

spent eight days, at the time of Goethe's eightieth birth- 
day, discussing, among many things, the latter's optical 
theories. This afforded the greatest pleasure to Goethe, 
as well as to Quetelet and his wife, and led to an un- 
usually felicitous correspondence. 1 

The following summer he made a four months' tour 
through Italy and Sicily, making the acquaintance of 
scholars and learned societies. On this trip, as also on 
the preceding, he made numerous observations on the 
strength of terrestrial magnetic currents. 2 

After his installation at the Observatory, in 1832, his 
life for the next forty-two years was devoted almost en- 
tirely to three major interests : the various lines of re- 
search carried on at the Observatory, the work of the 
Academy and his statistical inquiries. These three 
spheres of activity will be treated separately. 

At the Observatory a vast amount of research work 
was organized, dealing with astronomy, meteorology 
and physics of the globe. 3 Quetelet had always been 
interested in falling stars. In his doctor's dissertation 
he had defended Olbers's theory of the lunar origin of 
aeroliths. As early as 1826 he developed a method for 

: Quetelet has given two accounts of the sojourn at Weimar: " Notes 
extraites d'un voyage scientifique, fait en Allemagne pendant l'ete de 
1829," in the Correspo?idance , vol. vii, pp. 126-148, 161-178 and 225-239, 
and " Johann Wolfgang Goethe," in Sciences math, et phys. chez les 
Beiges au commencement du xixe Steele, pp. 656-669. There is another 
account, "Quetelet bei Goethe," in Festgabe fur Johannes Conrad 
(Jena, 1898), pp. 31 1-334- 

" Results published in Nouveaux mimoires, vol. vi, and Correspond- 
ance, vol. vi. He made a three months' trip through Italy and Tyrol 
beginning in August, 1839, at which time he gathered another series of 
magnetic observations. 

3 At the Observatory Quetelet had almost from the beginning two as- 
sistants, one of whom was Edward Mailly, the author of the Essai 
which has been the chief source for this sketch. 



465] BIOGRAPHICAL SKETCH 2 $ 

calculating the height of a meteor from two observa- 
tions. 1 This plan, being well received, enabled Quetelet 
to organize simultaneous observations in four Belgian 
cities. At this time we find him emphasizing what must 
be considered one of his most important contributions 
to the various fields of science in which he labored, 
namely, the necessity of simultaneous observations at 
different points. His introduction of it here into astro- 
nomical research was followed, as we shall see, by his 
development of it on a large scale in meteorological and 
physical research and by his efforts to secure uniform 
international statistics. At the same time he emphasized 
the necessity of correcting astronomical observations for 
the personal equation in order to render them com- 
parable. In 1836 his observations of falling stars led to 
the discovery that the nights of August ten and eleven, 
like those of November thirteen and fourteen, were con- 
spicuous for meteoric showers. 

Among other facts connected with his astronomical 
activity, we may note a series of observations of sunspots, 
begun in 1832; observations on tides on the coast of 
Belgium, undertaken at the request of Whewell in 1835 J 
the commencement, the same year, upon the initiative of 
Sir John Herschel, of hourly meteorological observa- 
tions at the time of the solstices and equinoxes, but, 
after 1841, made every two hours throughout the year; 
magnetic observations, begun in 1840 at the request of 
the Royal Astronomical Society of London, and made at 
five-minute intervals during one twenty-four hours each 
month; the erection from 1838 to 1839, at government 
request, of small telescopes in the five largest cities out- 

1 See Correspondance, vol. i, also Report of the British Association 
for the Advancement of Science, 1833, p. 489; 1835, p. xxxviii. 



24 ADOLPHE QUETELET AS STATISTICIAN [^ 

side of Brussels, and of sundials in forty-one towns, in 
order to guarantee uniformity of time throughout the 
kingdom; and the determination of the difference in 
longitude between Greenwich and Brussels. The publi- 
cation of the Annuaire and of the Ann ales of the Ob- 
servatory began in 1834. In 1854 a volume entitled 
Almanack skculaire was issued from the Observatory. 
After 1857 the. work of the Observatory was carried on 
largely by Quetelet's only son, Ernest, who became an 
accomplished astronomer and his father's successor as 
director. 

But Quetelet's dominant scientific interest seems to 
have been other than strictly astronomical. The study 
of meteorological and physical phenomena, especially 
their periodicity, absorbed much of his attention. These 
observations began with the temperature of the earth, 1 
and the intensity of atmospheric electricity and were ex- 
tended to include the variations of barometric pressure 
and periodic phenomena of the life of plants and animals. 2 
His study of atmospheric electricity and its annual and 
diurnal variations, established the law of the variation of 
intensity with height. This study was looked upon as 
of considerable importance by French, German and 
English scientists. 3 Wheatstone and Faraday made it 
the subject of special reports to the British Association 
and the Royal Society respectively. 4 

1 Suggested by Fourier's MSmoire sur les temperatures du globe ter- 
restre et des espaces planHaires (Paris, 1827). 

2 Many of these studies, first published in the Annates of the Obser- 
vatory and in the MSmoires of the Academy were brought together in 
Sur le climat de la Belgique (2 vols., 1849-1857). 

3 See Archives des sciences physiques et naturelles (Geneva, July, 
1849). 

4 See Report of the British Association (1849), vol. 19, "Transactions 
of the Sections," pp. 11-15. 



467] BIOGRAPHICAL SKETCH 2 $ 

More important by far were the observations of 
barometric pressures leading to the discovery of atmos- 
pheric waves. l He had conceived the advantage of 
simultaneous observations in various places in dealing 
with matters of climatology. Securing the assistance 
of scientists throughout Belgium, and later throughout 
Europe, he secured a mass of observations of hourly 
barometric pressures. When these were chartered they 
revealed the succession of variations in pressure due 
to atmospheric waves. This study 2 of the form, size 
and velocity of atmospheric waves was pioneer. When 
carried out on the basis of simultaneous international 
observations, this discovery led to most important 
consequences for our knowledge of storms and prob- 
able weather conditions. 3 A long stride was made 
toward international cooperation and uniformity by the 
Sea Conference, held at Brussels in 1853. 4 Ten states 
were represented and Quetelet was chosen president. 
Further advance was made in 1873 at the first Interna- 
tional Meteorological Congress, 5 an assemblage Quetelet 
had long desired to call. He was represented by his 
son, and his plan for the observation of natural phe- 
nomena was made the central theme of discussion. 

1 He was probably led to such research by the suggestion of Sir John 
Herschel. But Quetelet organized independently five stations in Bel- 
gium and later seventy scattered over central and western Europe, 
whose observations were forwarded and tabulated at the Brussels Obser- 
vatory. See Bulletins de V acad., 2nd Series, vol. xxxviii, p. 838. 

2 Published in the Annales of the Observatory, vol. viii, part I. 

3 See quotation, Mailly's Essai, p. 253, from the Annuaire de la 
society mHeorologique de France, 1867. 

* The suggestion for this conference came from Matthew Maury, of 
Washington. At his suggestion Quetelet induced the Belgian govern- 
ment to call the conference, "to establish a uniform system of meteoro- 
logical observations for the sea." Mailly, Essai, p. 224. 

s At the World's Exposition at Vienna. 



26 ADOLPHE QUETELET AS STATISTICIAN [ 4 68 

In close connection with these observations were those 
made on the periodic, annual and diurnal, phenomena of 
plants and animals. These had been begun in 1839 by a 
study of the time of blooming of flowers, and were ex- 
tended in 1 841 to include the time of foliation and of 
falling leaves. In this work, leading to many interesting 
and significant correlations, he enlisted the cooperation 
of scientists in every country of western Europe. For 
this purpose, Quetelet prepared in 1842 an extensive 
scheme of investigation 1 embracing meteorology, physics 
of the globe, and the annual and diurnal habits of plants 
and animals. 2 

De la Rive, in reviewing Sur la physique du globe? at- 
tributed the highest importance to these studies in mete- 
orological and terrestrial physics, placing Quetelet in the 
"first rank among meteorologists." 4 Reichesberg re- 
marks that there are few physicists who have advanced the 
development of meteorology and physics of the globe to 
such an extent as Quetelet. 5 The great merit of these 
studies is found in the admirable plan for the study of 
periodic phenomena, particularly in the continued insist- 
ence on the simultaneous observation of the same phe- 
nomena from many scattered points. He was the first to 
collect material in such manner and quantity as made 
possible the discovery of regularity where the human 

*For this plan see Bulletins de I'acad., 1st Series, vol. ix, part I, pp. 
65-95. 

' Results published annually in Nouveaux mimoires of the Academy 
beginning with vol. xv. 

3 Published in the Annales of the Observatory (1861), vol. xiii; also 
separately Brussels, 1861. 

* Archives des sciences physiques et naturelles (Geneva, 1862, vol. xv, 
July). 

5 " Der beruhmte Statistiker," p. 442. 



469] BIOGRAPHICAL SKETCH 2 J 

mind had previously found only chance. The wonderful 
scientific imagination of the man is strikingly shown in 
his conception of a world physics as presented in his 
Sur la physique du globe and his Mktkorologie de la 
Belgique compare" e a celle du globe. ] Here was a vast 
conception, embracing in its realization the most com- 
plete observations of the magnetic, meteorological, 
animal and vegetable phenomena of the entire earth on a 
systematic and uniform basis with a view to discovering 
the order in a vast mass of apparently disordered events. 
We take up now Quetelet's connection with the Acad- 
emy. Chosen to membership in 1820, he soon came to 
play a leading role in its activities. He was named 
director for the years 1832 and 1833, and was chosen 
perpetual secretary in 1834. This office he held for forty 
years, during which he was the "guiding spirit'' 2 of the 
Academy. " He so ruled his little republic as to secure 
the regard, esteem and veneration of all within its walls, 
. . . " 3 At his suggestion, the Academy began the publi- 
cation of its Bulletin in 1832, and three years later, as 
secretary, he brought out the first volume of the A11- 
nuaire. When the Academy was reorganized in 1845, 4 
Quetelet secured the addition of the class of Beaux- 
Arts. 5 This he had attempted in 1832. Having failed 

Brussels, 1867. 

2 Mouat, "Monsieur Quetelet," Jour. Stat. Soc. of London, vol. 
xxxvii, p. 114; see also "Discours," pronounced at Quetelet's funeral, 
Bulletins de V acad., 2nd Series, vol. xxxvii, p. 249. 

3 Mouat, loc. cit. 

4 It was known as "l'Academie royale des sciences et belles-lettres 
de Bruxelles " until 1845, and since then as "l'Academie royale des 
sciences, des lettres, et des beaux-arts de Belgique." 

5 He seems to have had a natural and decided taste for art. He first 
came into public notice as a youth through the exhibition of the prize 
drawing at the Lyceum at Ghent in 1812. 



2 g ADOLPHE QUETELET AS STATISTICIAN [470 

he contented himself with assisting in the organization 
of the Cercle artistique et littkraire, of which he was for 
some time the president. As secretary of the Academy 
he was always prompt and painstaking in fulfilling his 
duties. Fifteen days before his death, though already 
suffering from his death malady, he attended the session. 
" In his appreciations of the works of his fellows, he was 
usually fair-minded, but superficial." ! Many of his own 
articles were first published by the Academy, and it was 
largely through the medium of the Academy that Quete- 
let became the stimulator of a new intellectual life in 
Belgium. There are many testimonials to his stimulating 
influence. He was declared, at his death, to be virtually 
the creator of the Academy, as also of the Observatory 
and other scientific and educational institutions, all potent 
in the intellectual regeneration of Belgium. 2 

But, though Quetelet's influence in and through the 
Academy and his researches in meteorology and terres- 
trial physics are of importance, he became known to the 
world through, and will be remembered chiefly for, his 
statistical studies. After 1825 his articles dealing with 
every phase of statistics became more and more promi- 
nent among his various publications. Since these writ- 
ings are to be studied in some detail in later chapters, 
we will give here a sketch only of his practical activity 
with reference to official statistics. 

Upon the formation of the statistical bureau of Hol- 
land under Smits, in 1826, Quetelet became correspond- 
ent for Brabant. He at once urged that a census be 
taken and assisted in formulating plans for the census of 
1829. The results of this census were published 

1 Mailly, Essai, p. 261. 

2 See "Discours," pronounced at his funeral, Bulletins of the Acad- 
emy, 2nd series, vol. xxxvii, pp. 244-266. 



4 7 1 ] BIOGRAPHICAL SKETCH 29 

separately in each country after the revolution of 1830. ' 
He later became supervisor of statistics in the adminis- 
tration, and in 1841 he was instrumental in the organiza- 
tion of the Commission centrale de statistique. This 
Commission, of which he was president until his death, 
supervised the subsequent censuses, organized the work 
of the provincial commissions, and brought the Belgian 
statistics to a standard of completeness and reliability 
that was pre-eminent. Wolowski said, in 1874, that 
"the success of the Commission, thanks to Quetelet, 
was so great that many nations . . . hastened to found 
a central commission of statistics patterned after that 
which he had founded. " 2 

Meanwhile, as official Belgian delegate to the meeting 
of the British Association at Cambridge, in 1833, he had 
been the immediate cause of the formation of a statistical 
section. 3 This section was put in charge of a permanent 
committee, having Babbage as chairman and Quetelet as 
one of its members. Quetelet considered the scope of 
this section too narrowly limited by the rules of the 
Association. " He accordingly suggested to M. Bab- 
bage, from whom we have the statement, the formation 
of a statistical society in London." 4 This society was 

1 Recherches sur la reproduction et la mortalitS de Vhomme aux differ- 
ent s ages, et sur la population Belgique {premier recueil officiel) par 
MM. Quetelet et Smits (Brussels, 1832). 

s "£loge de Quetelet," Jour, de la soc. de sta. de Paris, vol. xv, 
p. 120. 

3 See Report of the British Association, 1833, p. 484; also Quetelet, 
" Notes extraites d'un voyage en Angleterre en 1833," Correspondance, 
vol. viii. 

*F. J. Mouat, " History of the Statistical Society of London," Jour. 
Sta. Soc. of London, Jubilee vol., pp. 14-15. See also in the same Journal, 
vol. i, p. 4; vol. xxxiv, p. 412, and vol. xxxvii, pp. 309 and 415; and 
F. X. Neumann-Spallart, " Apergu historique," in the Bulletin de V In- 
stitut international de statistique , vol. i, pp. 1-2. 



3 o ADOLPHE QUETELET AS STATISTICIAN [ 4 ^ 2 

founded March 15, 1834, and the same year Quetelet 
was elected a corresponding member of the British Asso- 
ciation. 

The need of international uniformity and comparability 
of statistical data impressed itself deeply upon Quetelet, 
as had the similar need with respect to astronomical and 
meteorological data at an earlier date. 1 With character- 
istic zeal he sought to bring about the practical realiza- 
tion of this highly important end. The idea of inter- 
national cooperation, bearing the approval of the Com- 
mission centrale, was presented to a group of scientists 
at the Universal Exposition at London in 185 1. The 
project met with heartiest approval. Brussels was desig- 
nated as the place of meeting for the first session because 
of the excellence of the Belgian statistics. Further pro- 
ceedings devolved on the Commission centrale. A com- 
mittee was chosen to draw a plan of organization, pre- 
pare rules of order and propose questions. As chairman 
of this committee, Quetelet became the moving and di- 
recting force in what followed. The government was 
induced to issue invitations to an International Statistical 
Congress, plans of organization were drawn providing 
for three sections, and a set of eleven questions was pro- 
posed for discussion. At the first session of the Con- 
gress, Brussels, 1853, Quetelet was chosen president, and 
in his opening address he dwelt upon the advantages of 
international uniformity in plans, purposes and termini- 
ology of the official statistical publications. 

The Congress was a decided success and other sessions 
followed. The influence of this Congress on both the 
theory and practice of statistics was immense. Meitzen 2 

ipp. 23 and 25, supra. 

5 August Meitzen, History, Theory and Technique of Statistics, tr. by- 
Roland P. Falkner, Supplement to Annals of the American Academy 
of Political and Social Science (March, 1891), p. 81. 



4 7 3 ] BIOGRAPHICAL SKETCH 3! 

says, "Everything which has occurred for statistics 1 
since the beginning of the Congress has been essentially 
a consequence of its stimulating and invigorating influ- 
ence." Ficher, in opening the Statistische Monatschrift* 
with a sketch of Quetelet, says " International Statistics 
will ever remain Quetelet's most splendid creation." 
Quetelet was a prominent figure at all but two sessions 
of the Congress; 3 Wolowski tells us that "it was always 
the spirit of Quetelet that animated them." 4 We see 
him at the age of seventy-six, upon urgent request, re- 
pairing to St. Petersburg to the last but one of these 
sessions. And we see him returning, refreshed and re- 
juvenated by the splendid ovation he had received. 5 This 
was one of his greatest triumphs and was to him a 
source of deepest gratification. 

Before closing this sketch, mention should be made of 
an attack of apoplexy from which Quetelet suffered in 
the summer of 1855. He was stricken suddenly while 
studying on the veranda of his home at the Observatory. 
He recovered strength in a few weeks to resume his 
labors, but his intellect had lost its acuteness, his memory 
its certainty and his literary style much of its beauty and 
eloquence. His writings, for a long time, needed the 
most thorough revision. Mailly, who was one of his 
assistants at this time, tells us that he would use the 
same word over and over again, and would express the 
same thoughts with monotonous repetition. He even 

1 Meitzen must mean official statistics. 

3 Vienna, 1875, vol. i, p. 13. 

'Paris, 1855, and the session after his death, Budapest, 1876. 

*"£loge de Quetelet," Jour, de la soc. de sta. de Paris, vol. xv, 
p. 120. 

5 See " Obituary Notice," Jour. Stat. Soc. of London, vol. xxxvii, p. 
US- 



32 ADOLPHE QUETELET AS STATISTICIAN [474 

constructed sentences whose ends bore no relation to 
their beginnings, and, when such were corrected, Quetelet 
would be unconscious of change. 1 His books published 
after 1855, in so far as new in composition, are full of 
ambiguous or unintelligible phrases, ill-arranged and 
vefy repetitious. This is notably true of his histories of 
1864 and 1866, 2 and his works on meteorology, 3 as well 
as of some of his statistical writings. His affliction was in- 
tensified by the death of his wife and of his only daughter. 
Yet, in time, he very largely regained his former eager- 
ness of spirit and worked on to the end with unabated 
intensity and care. In his latest years, further saddened 
by the loss of some of the younger spirits about him, he 
became more and more absorbed in his daily labors. He 
had for so many years guided the work of the Academy 
and the Observatory, that it is little to wonder at, that 
they were the burden of his incoherent mumblings in the 
brief spell of deliriousness preceding his death. 

His life was crowned with honors. He was a member 
of more than one hundred learned societies, and had been 
decorated with the badges of many royal and honorable 
orders of all lands. Among the learned societies were 
academies of science, institutes, royal societies, and medi- 
cal, statistical, geograplical, meteorological, anthropo- 
logical, philosophical, physical and astronomical societies 
the world over. 4 The Acadkrnie des sciences morales et 

1 Mailly, Essai, p. 266, and Reichesberg, " Der beriihmte Statis- 
tiker," p. 460. 

2 To those mentioned in note p. 16, supra, should be added Premier 
siecle de I 'acadimie (Brussels, 1872). 

3 Among these were: Sur le climat de la Belgique (Brussels, 2 vols., 
1849-1857); Physique du globe {ibid., 1861); MttZorologie de la Belgique 
compare" e a celle du globe {ibid., 1867). 

4 Ficher, Statistische Monatschrift, vol. i, p. 13, says that, aside from 



475 ] BIOGRAPHICAL SKETCH 33 

politiques of Paris bestowed upon him its highest honor 
by electing him an associate in 1872. At the same time 
the Academy of Sciences of Berlin hailed him as " the 
creator of a new science." 1 Reichesberg observes that 
as the founder of a new statistics he developed the scien- 
tific method by which the laws of social life may be dis- 
covered, and thus established the foundation of a new 
science, Social Physics, as he himself called it, or Soci- 
ology, as it is customarily called today. 2 Doubtless one 
of Quetelet's greatest merits lies in his development of 
moral statistics. Of this development two features are 
of lasting significance. One of these is the deA^elopment 
of a method of investigation having a mathematical basis 
in the theory of probabilities. The other is found in the 
emphasis on the word moral. Others had studied birth, 
death and marriage statistics, but Quetelet was the first 
to perceive in such studies a field that could be expanded 
to include the whole nature of man and the characteristics 
of human society. The simple proposition that the 
moral nature of men and the qualities of a group of men 
can be best determined by a statistical study of their 
actions was exalted by him into the foundation of exact 
social science. 

Quetelet's personality is represented as most winning. 
Modest and generous, convinced but respectful of others' 
opinions, always calm and considerate, a man of broad 
learning and an attractive conversationalist, he won and 
kept friends wherever he went. A man of excellent tact, 

learned societies of Belgium, he was a member of ninety-six in Europe, 
one in Asia, one in Africa, and nine in North and South America. For 
a list of these societies see Bulletins de Vacad. roy. de Belg., 2nd series, 
vol. xxxvii, pp. 246 and 265. 

1 Bull, de Vacad., 2nd series, vol. xxxvii, p. 257. 

a "Der beriihmte Statistiker," pp. 443-444. 



34 ADOLPHE QUETELET AS STATISTICIAN [476 

as well as of tremendous enthusiasm, he readily enlisted 
support for many schemes of cooperative scientific 
endeavor. A man of wide intellectual interests, and at 
the same time, endowed with a prodigious capacity for 
labor, he contributed to the advancement of several 
sciences, aroused anew the entire intellectual life of his 
country and stimulated the activity of artists and scien- 
tists throughout the world. Until the attack of 1855, he 
is represented as always animated and genial, fond of wit 
and laughter. " Rabelais was almost as dear to him as 
Pascal." r 

His home life was of marked beauty and serenity. He 
found great pleasure in his two children, and the astro- 
nomical ability of his son was a source of great pride to 
him. Quetelet was himself a modest musician, and his 
wife an accomplished one. Friends were regularly en- 
tertained at dinner on Sundays, and Sunday evenings 
were usually given over to music and charades. Per- 
sonally acquainted with the leading scientists of his time, 
he exercised the most generous hospitality in the home 
at the Observatory. Distinguished men, coming to 
Belgium from any of the European capitals or centers of 
learning, brought letters of introduction to Quetelet and 
were always assured a gracious reception by him. One 
of the speakers at his funeral said of him, "as a man of 
science he was admired ; in political affairs he was re- 
spected ; in private life he was beloved." 3 

He died on the seventeenth of February, 1874, and was 
buried with honors fitting one of earth's nobility. His 
funeral was the occasion of a most numerous and dis- 
tinguished gathering of members of royal families, 

1 Mailly, Essai, p. 262. 

' x Bulletins of the Belgian Academy, 2nd series, vol. xxxvii, p. 261. 



4 77] BIOGRAPHICAL SKETCH ?,$ 

scientists, men of letters and representatives of learned 
societies. Funds for a statue of him were soon raised 
by popular subscription, the monument being unveiled 
at Brussels in 1880. He is represented seated in an arm- 
chair, the fingers of his left hand spread out on a nearby 
globe; his right arm rests on the arm of the chair and 
his head is raised as he peers into the secrets of space. 1 

The extent of Quetelet's scientific activity was so great, 
covering as it did the various fields of mathematics, 
astronomy, physics and statistics, that his rank among 
men of science is difficult to estimate. It may be said 
without fear of contradiction that few men have so 
largely contributed to the spread of scientific knowledge 
or stimulated such wide and persistent discussion and 
inquiry as did he. One historian says of him, " In the 
history of natural science, Quetelet will, with good right, 
be placed in the rank of Pascal, Leibnitz, Bernoulli, La- 
place, Poisson and such scientists. " 2 

1 Reichesberg, " Der beriihmte Statistiker," p. 460. 

2 Von John, Geschichte der Statistik, p. 335. 



CHAPTER II 

QUETELET IN THE HISTORY OF STATISTICS 

It is proposed in this chapter to relate Quetelet to 
the historical development of statistics previous to 1825, 
when he began to show some statistical activity. This 
development can be traced through two series of writ- 
ings, showing different conceptions and methods. One 
series includes the works by Muenster, Conring and 
Achenwall and his disciples ; the other, works by Graunt, 
the School of Political Arithmetic, Derham and Suss- 
milch. Those of the first series embrace the whole life 
and organization of the state as their object, and rely on 
verbal analysis and description. Those of the second are 
relatively limited in scope and use enumeration and calcu- 
lation as distinctive methods. The conception, scope and 
method of each of these two classes of statistical writings 
will be briefly traced, and Quetelet's contribution to their 
further development and transformation stated. 1 

Since nations began there have been records of a sta- 
tistical character. The rise of modern nations, with the 
growing sense of national unity and of international 
jealousy, gave rise to comprehensive descriptions of 

1 For general guidance the following works have been used: Von John, 
Geschichte der Statistik, erster Teil, von dem Ur sprung der Statistik 
bis auf Quetelet (1835), (Stuttgart, 1884); August Meitzen's History- 
Theory and Technique of Statistics, tr. by Roland P. Falkner, Supple, 
ment to Annals of the American Academy of Political and Social Sci- 
ence, March, 1891. 

36 [478 



479] Q UETELET IN THE HISTORY OF STATISTICS 37 

nations and estimates of their relative resources in men 
and materials of war. Meitzen l finds the first of these 
in the Cosmographia (1536 and 1544) of Sebastian 
Muenster. This work treated systematically Europe, 
Asia and Africa, covering the geography, history, man- 
ners and customs, industries, commerce, political and 
ecclesiastical organization, and military power of all 
known countries. This was followed by others of the 
same nature, 2 which furnished the basis for the develop- 
ment of statistics as a discipline in the German universi- 
ties. The first university lectures of such character were 
those of Herman Conring 3 (1606-1681). These lectures 
were begun at the University of Helmstadt in 1660 and 
were published first in 1668, but in best form, post- 
humously in 1730. 4 Volume four of the latter edition 
treats of " Statskunde" or " notitia rerum publicanim." 
According to Conring the notitia rerum publicarum 
treat of the condition of individual states in whole or in 
part, and properly should be confined in time to the 
present. The chief aim is to gain a knowledge of the 
state for the guidance of practical statesmen. For this 
reason they treat not only facts, but causes. Conring, 
being scholastic in his treatment, gives as causes the 
Aristotelian classification. The material causes are land 
and people; the formal and final are the kinds of union, 
such as government and administration, with reference 
to special objects of state; and the efficient causes are the 
revenues and land and sea power. Coming's work is 

x Op. cit., p. 20. 

"See especially Von John, op. cit., p. 34, ei seq. 

3 Meitzen, p. 21; John, p. 52; Block, Traite" th&oretique et pratique de 
statistique (2nd ed., Paris, 1886), pp. 4-5. 

* This work was entitled Exercitatio historico-politica de notitia singu- 
laris alicujus reipublicae. 



38 ADOLPIIE QUETELET AS STATISTICIAN [ 4 go 

worthy of much emphasis. It was the first notable 
attempt at the systematic presentation of both the theory 
and the material of political statistics. The form he gave 
to such presentation was lasting. John observes that "a 
comparison of the theories set forth a century later by 
Achenwall, Von Schlozer and followers always discloses 
again this scholastic system formulated by Conring." 
For this reason " the great German poly-histor of the 
seventeenth century can alone be called the ' father ' of 
this 2 form of statistics." 3 

Meitzen, however, falls in with the custom by desig- 
nating Achenwall (1719-1772) "the father of statistical 
science." 4 Achenwall tells us 5 that his first statistical 
work was his Vorbereitung zur Statswissenschaft der 
europaischen Reiche, published in 1748. This appeared 
as the introduction of a work of the year following, enti- 
tled Abriss der Statswissenschaft der europaischen 
Reiche. 6 

The advance of Achenwall over his predecessors was 
in more systematic treatment and more exact definition. 
This is evidenced by the manner in which he takes up 
the theoretical problems. " Before we begin to observe 
the constitution of the most important European states 
of to-day, it will be fitting to make some general remarks 

l Op. cit., p. 61. 

*The word " this " evidently refers to the German university statistics. 

3 Ibid., p. 70. 

i Op. cit., p. 22. See Block, op. cit., p. 7. 

5 Statsverfassung der heutigen vornehmsien europaischen Reiche und 
Volker im Grundriss, edited by M. C. Sprengel (Gottingen, 1st pt., 
1790, 2nd pt., 1798), Vorrede zur ersten Ausgabe. 

8 This ran through five editions in the author's lifetime; a sixth was 
brought out by Von Schlozer in 1781. References here are to the sev- 
enth edition by Sprengel, the St atsver fas sting mentioned in the pre- 
ceding note. 



481] QUETELET IN THE HISTORY OF STATISTICS 39 

on ' Statistik,' 1 as that discipline which is concerned with 
this object; to set forth its meaning, limit and divisions 
and its natural connections ; as also to indicate briefly 
the uses, the history and the sources of the same." 2 In 
observing a state, Achenwall says that he finds many 
things which notably advance or hinder its prosperity. 
"Such things can be called Statsmerkwurdigkeiten " 3 
(the noteworthy things of a state). " The totality of the 
actual ' Statsmerkwurdigkeiten ' of a kingdom or repub- 
lic makes up its constitution in the broadest sense; and 
the account of the constitutions of one or more states, 
treated individually, is 'Statistik, (Statskunde), oder 
Statsbeschreibung.'" 4 'Statistik' studies the life of a 
state with a view of ascertaining its sources of weakness 
and strength. 5 It will not include all facts of interest 
regarding a state, but only such as are important for 
" politische Kenntniss," 6 that is, 'Statistik' seeks to ob- 
tain, through a description of the state, a guide for the 
statesman. 7 Though thus limited, ' Statistik ' still in- 
cluded much that later became differentiated, as geogra- 
phy, ethnography, public and administrative law and 
political economy. Achenwall's work was translated into 
many languages and his definition of statistics thus came 
into general use. 

' Statistik ' thus owed the fixity of its definition to 
Achenwall, but there was little change in the real char- 
acter of the discipline from the very early time of Muen- 
ster to the beginning of the last century. Von Schlozer 
epitomized the definition, 8 and he and other representa- 

1 He first uses this word in the " Vorrede " of the first edition. 

2 Vorbereitung, p. 2. * Ibid., p. 4. * Ibid., p. 5. 
°Ibid.,p.6. * Ibid.,?. 6. ' Ibid., p. 46. 

8 ' ' Statskunde ist eine stillstehende Statsgeschichte ; so wie diese eine 
fortlaufende Statskunde," ibid., p. 5, in brackets. 



4 ADOLPHE QUETELET AS STATISTICIAN [ 4 g 2 

tives of the school made such improvement in the analy- 
sis and arrangement of results as the continued enrich- 
ment of material suggested. Both the theory and the 
method were simple. This school of statisticians be- 
lieved the possibilities of their science were exhausted by 
a verbal description of a contemporary social condition, 
so arranged as to be useful to statesmen, and accompan- 
ied by general observations on the results. But an 
almost revolutionary change was impending. A symp- 
tom of this change is found in the works of Ancherson * 
(1741) and Biisching 2 (1758). Though Achenwall had 
stated that knowledge of the strength of a nation would 
require a comparison of its resources with those of other 
nations, 3 these men were the first to make such compari- 
sons directly. Moreover, they used, so far as possible, 
numerical tables drawn from official sources. Besides, 
Biisching gave slight space to the geography, constitu- 
tion and administration of the countries described and 
emphasized the economic and material factors of social life. 
But the real change followed the establishment of 
statistical bureaus and the publication by them of the 
results of censuses and inquiries. " Die Tabellen-Statis- 
tik' 5 quickly came into vogue. A tragic, but bloodless, 
warfare ensued between the orthodox statisticians and 
the worshipers of rows of figures. 4 The latter had the 
assistance of continuous new recruits in the form of large 
quotas of official numerical data, which could not fail of 

1 Von John, op. cit., p. 88. 

2 Meitzen, op. cit., p. 24, et seg., and p, 41. 

a Vorbereihcng, pp. 47-48. 

*The followers of Achenwall claimed that their statistics were "the 
right eye of political science," and accused the table statisticians of re- 
ducing statistics to a "veritable cadaver, on which one could not look 
without abhorrence," Von John, op. cit., p. 129. 



4 83] QUETELET IN THE HISTORY OF STATISTICS 4I 

effect. When the atmosphere cleared it was found that 
a considerable change had been wrought in the character 
of descriptive statistics. ' Statistik ' disappeared as a 
university discipline and was replaced by two rather dis- 
tinct kinds of descriptive material in which numerical 
tables and verbal explanation divided honors. These 
two were the official statistical publications, and the 
statistical compendiums prepared mostly by private en- 
terprise. 

Much of Quetelet's activity was connected with per- 
fecting these two kinds of statistical works. His own 
definition of statistics * evidently restated that given by 
Achenwall and Von Schlozer, and the objects of statisti- 
cal inquiry, as given by him 2 were those treated by this 
school. But we shall see that it was primarily his own 
activity that led to the conception of statistics as a 
method of observation based on enumeration and ap- 
plicable to any field of scientific inquiry. It is impossible 
to state just what elements in the betterment of descrip- 
tive statistics were due uniquely to Quetelet, but he con- 
tributed to the development in the following ways: (i) 
perfection of plans for census taking; (2) criticism of 
sources; (3) arrangement of materials; and (4) pro- 
gress toward uniformity and comparability of data. 

Quetelet's direct interest in public statistics dates from 
his appointment in 1826 as correspondent for Brabant to 

1 Letters on the Theory of Probabilities , as Applied to the Moral and 
Political Sciences, translated from the French by O. G. Doivnes (Lon- 
don, 1849), pp. 176, 179, 180, 182. 

*Ibid,, p. 183. Note also headings treated in " Recherches statis- 
tiques sur le royaume des Pays-Bas," Nouveaux mimoires de V acad- 
imie royale des sciences et belles-lettres de Bruxelles, vol. v (1829), and 
the elaborate Statistique Internationale ', Bulletin de la commission cen- 
trale de staiistique (Bruxelles), vol. x (1866). 



4 2 ADOLPHE QUETELET AS STATISTICIAN [484 

the statistical bureau of Holland. His connection with 
the early censuses of Holland (1829) and of Belgium 
(1832), his position as supervisor of the statistics of the 
administration and later as president of the Com?nissio?i 
ce?itrale, made it possible for him to impress a high 
character of excellence on the statistical publications of 
his own country. He gave careful consideration to the 
collection of data, both as to the blank forms to be used 
and as to the nature of the questions to be asked, to the 
tabulation and forms of presentation of the material, to 
methods of averaging and summarizing data, and to the 
criticism, both of the sources and of the results of the in- 
vestigation. 

The practical rules developed by him still form the 
essential guides in census taking. 1 His predecessors had 
given some attention to the criticism of results, but 
Quetelet assisted materially in the advance of criticism 
of sources. " Statistics are of value only according to 
their exactness. Without this essential quality they 
become useless, and even dangerous, since they conduce 
to error." 2 He insisted that every statistical work 
should give both the sources of the data and the manner 
of their collection. The checking of statistical documents, 
he held, should be both moral and material. 3 By moral 
examination he meant an inquiry into the influences 
under which the data are collected and the nature of 
their sources. The material examination consists in 
observing whether the numbers are sufficiently large to 
assure the predominance of constant causes, and suffi- 
ciently continuous or uniform to make certain that acci- 
dental causes have not unduly influenced some of them, 

1 See Letters, p. 195, et seq. 

-Ibid., p. 198. '''Ibid., " Letter xxxix." 



485] QUETELET IN THE HISTORY OF STATISTICS 43 

and whether they have been combined with mathematical 
accuracy. As to the arrangement and presentation of 
results, Quetelet made progress both in official docu- 
ments, so as to secure clearness and ready comprehensi- 
bility, and in scientific studies, so as to show the greatest 
possible number of correlations. To group the data so 
that permanent factors would be thrust into prominent 
view, and so as to make comparisons on the basis of 
time, place, sex, age, etc., easily possible, were essential 
principles with him. The study of correlations, the 
attempt to find the causal relations of phenomena, marks 
a very great advance over the works in this particular 
line of statistical development. Such studies required 
the development of a more precise technique, which, in 
turn, reacted on the criticism of sources and gave to 
descriptive statistics a deeper significance. It is pre- 
cisely at this point that descriptive statistics felt most 
decisively the influence of the statistics begun by the 
School of Political Arithmetic. And it is in and through 
the work of Quetelet that this influence was first clearly 
exerted. That is, the development of official statistics 
furnished more abundant numerical data, and the elabo- 
ration by Quetelet of a method for treating such data 
made possible the correlation of statistical results with 
economic and social conditions and the consideration of 
questions involving the public weal. The disciples of 
Achenwall had upbraided the table statisticians with 
neglecting the consideration of the deeper questions of 
social life. They failed to recognize the necessity of 
precise data, of number and measure, in order to draw 
reasonably correct and at the same time significant con- 
clusions on such questions. 

Finally Quetelet contributed to the progress toward 
uniformity and comparability in official statistics. By 



44. ADOLPHE QUETELET AS STATISTICIAN [486 

comparability he meant two things, namely, (1) uni- 
formity of all data collected under a given schedule for 
one time and place, and (2) uniformity of all data under 
a given schedule for different times and places. 1 Uni- 
formity of the first sort is absolutely essential to the 
validity of any conclusions whatever. Uniformity for 
different times makes possible the measurement of the 
change in a social condition within a nation through a 
period of time, while uniformity for different countries 
makes possible the direct comparison of social conditions 
in these countries. Quetelet would not only test the 
progress of his own country but he dreamed of present- 
ing in comparable data the status and the progress of 
all nations. Hence his leadership in the organization of 
the International Statistical Congress. In his opening 
address, as well as in the formulation of the plans for the 
first session, Quetelet sounded the keynote of this move- 
ment in his emphasis on international uniformity. He 
felt keenly the need of comparability among the official 
statistics of western nations. This end was to be realized 
through the collection of material on the basis of a com- 
mon plan, following similar instructions, classifications 
and schemes of presentation and using the same termin- 
ology. This end is still far from realization, but there 
can be little doubt that through this Congress Quetelet 
influenced, directly or indirectly, the statistics of many 
nations. The value to science of the realization of inter- 
national uniformity would be immense, inasmuch as it 
would make possible a multitude of correlations and 
comparisons that are now either dangerous or altogether 
impossible. 

Another line of statistical development gave rise to 

1 Letters, p. 177. 



4 8^] QUETELET IN THE HISTORY OF STATISTICS 45 

very different conceptions and methods. In 1662 Cap- 
tain John Graunt, F. R. S. (1620-1674) presented to the 
Royal Society his Natural and Political Observations 
upon the Bills of Mortality with reference to the Govern- 
ment, Religion, Trade, Growth, Air, Diseases, and the 
several cha?tges of the City of London. l This work has 
not been sufficiently emphasized by the historians of 
statistics. As a scientific study of population it was not 
surpassed until the appearance of Siissmilch's work, 
eighty years later. It contains the first presentation of 
a number of the inductions from population statistics, 
which Quetelet presented much more convincingly and 
impressively in Sur Vhomme, published in 1835. Graunt 
found that the deaths due to various diseases and even 
to certain kinds of accidents " bear a constant proportion 
unto the whole number of burials." 2 He pointed out the 
constancy in the number of abortions and still-births; 3 
the variation of the death rate by seasons ; 4 the ratio of 
births to deaths in city and in country ; 5 and the ratio of 
male to female births ; 6 he also presented the rough out- 
line of a table of mortality. 7 

The interesting feature of Graunt's work is not the ap- 
proximate accuracy of his conclusions, but the method 
he followed. He was permeated with the Baconian 
philosophy and sought truth through observation rather 
than speculation. His conclusions were faulty both be- 
cause of the incompleteness of his data and his utter lack 
of comprehension of the law of large numbers. His 
mortality table is, in fact, only a piece of rational guess- 
work. But his book stimulated the widest interest, and, 

References here are to the 5th edition, London, 1676. 

% Ibid., p. 26. z Ibid., p. 41. *Ibid., p. 56. 

3 Ibid., p. 57, et seq. (i Ibid., pp. 87, 103-104. 7 Ibid., pp. 83-84. 



4 6 ADOLPHE QUETELET AS STATISTICIAN [ 4 gg 

above all, opened the way for a new method of studying 
social life, namely, observation, enumeration and calcula- 
tion. It is with Graunt, in fact, that we find the begin- 
ning of statistics as a method of observation in the service 
of inductive social science. 1 

Petty's first researches were stimulated by Graunt's 
Observations, which he designated as "a new light to 
the world." 3 Petty was dominated by the same empir- 
cal philosophy; he would "use only arguments of 
sense," and would express himself in terms of "number, 
weight and measure." 3 Owing to the dearth of accurate 
enumerations he resorted to calculation, as, for example, 
the estimation of the number of inhabitants from the 
number of houses, or from the number of deaths. He 
appreciates the value of an average of several such com- 
putations, and "pitched the medium" 4 between extreme 
estimates. 

The cultivation of Political Arithmetic, " the art of 
reasoning by figures upon things relating to govern- 
ment," 5 was continued, notably, by Davenant, Arbuthnot 
and King. The essays of these writers were used by Sir 
Wm. Derham, F. R. S., in his Physico-Theology; or a 
Demonstration of the Being and Attributes of God from 
his Works of Creation. 6 This work is an elaborate argu- 

1 For an excellent estimate of Graunt's influence see The Economic 
Writings of Sir Wm. Petty (Cambridge, 1899), by Chas. H. Hull, vol. i, 
pp. lxxv-lxxix. He traces this influence through Derham, Siissmilch 
and Malthus to Darwin. 

- Observations upon the Dublin Bills of Mortality (1681), to be found 
in Several Essays in Political Arithmetick (London, 1659), p. 55. 

s Ibid. , ' ' Preface . ' ' * Ibid. , p . 1 23 . 

6 Davenant, Discourses on the Public Revenues, and on the Trade of 
England (London, 1698), pt. I, "Discourse I," p. 2. 
6 London, 1699. 



489] QUETELET IN THE HISTORY OF STATISTICS 4 y 

ment from design. He finds in the admirable propor- 
tions of marriages to births, of births to deaths, of males 
to females, the surest evidence of "the work of One that 
ruleth the World." 3 The perusal of Derham's Physico- 
Theology by Siissmilch, led him to undertake researches 
on the number of births, deaths and marriages according 
to the lists of the city of Breslau. 2 Meanwhile, he sent 
to England for the writings of Graunt and Petty. 3 His 
writings, especially the second edition, 4 proved to be a 
great advance upon the preceding, not only in the variety 
and exactness of conclusions, but also in the clearer con- 
nection between the concrete phenomena of social life 
and economic conditions. 

Moreover, he made distinct advances in method. 
Upon those wishing to controvert his conclusions he 
imposes the following conditions : 

(1) The lists must be correct, else contradiction is of no 
value. To this end it is necessary to consider well the condi- 
tions and changes of a place, to see whether war, plague or 
other disease has wrought any variation. (2) The numbers 
must not be small ; the greater they are and the more years 
included thereunder the better. ... If I have a hundred 
cases in support of my conclusion, then can nothing to the 
contrary be drawn from one case. 5 

It was, in fact, only by observing large numbers that he 

x Eighth edition (London, 1727), bk. iv, chap. 10, "Of the Balance 
of Animals or the Due Proportion in which the World is stocked with 
them." 

2 Die gottliche Ordnung in den Veranderungen des menschlichen 
Geschlechts (Berlin, 1st ed., 1742), " Vorrede," p. 13. 

3 /did., p. 16. 

4 2 vols., Berlin, 1761 and 1762. 

5 First edition, "Vorrede," pp. 38-39. 



48 ADOLPHE QUETELET AS STATISTICIAN [ 4 g 

could ascertain the great regularities in mathematical 
ratios which represented to him " the rules of order 
which God's wisdom and goodness have established." 

These quotations show Siissmilch's recognition in a 
general way, of three principles highly important for the 
development of statistical method, namely, (i) Social 
phenomena have causes; (2) the regularities found in 
statistical results reveal the rules of the existing social 
order; and (3) constancy in results can be obtained only 
by viewing large numbers. 2 All of these principles are 
found in the work of Quetelet. It required only a 
change from a theological to a scientific viewpoint to 
expand the first of these principles into a complete denial 
of chance and the assertation of an absolute solidarity in 
the sequence and the co-existence of social phenomena. 
Such a view became a philosophical tenet, and was a 
favorite doctrine of Quetelet's great friend and teacher, 
Laplace. It appears in Quetelet's writings in the form, 
"effects have causes and are proportioned to them," a 
form which suggests the theory of probabilities. The 
second of the above principles remained without emphasis 
until Quetelet sought to find in the statistical regulari- 
ties the laws of a social mechanics. The third was defin- 
itely recognized in the construction of mortality tables 
by Halley, Deparcieux, Wargentin and Kersseboom, and 
was well established as the "law of large numbers" by 
the development of the mathematical theory of prob- 
abilities. 

Coming down to the early years of Quetelet's life we 
find the most significant influences on the course of de- 
velopment of the statistics of population and of statistical 

1 Second edition, vol. i, title page. 

3 On this see ibid., vol. ii, pp. 262 and 408. 



491 ] QUETELET IN THE HISTORY OF STATISTICS 49 

method in the works of Malthus, Laplace and Fourier, 
all of whom Quetelet knew personally. Malthus's Essay 
on Population, though apparently not influenced by 
Sussmilch's Gbttliche Ordnung, gave a world-wide stim- 
ulus to the study of population in its economic and social 
aspects. Laplace continued the development of the the- 
ory of probabilities and instructed Quetelet therein. 
Fourier's influence was exerted through the Recherches 
statistigties sur la ville de Paris et le department de la 
Seine} The first four volumes of this series have intro- 
ductory essays by Fourier of very great value. In the 
first of these, Notions gfatkrales sur la population? he 
develops both algebraic and geometrical expressions for 
tables of population and of mortality, average duration 
of life and expectation of life, assuming the population to 
be stationary. He points out the greater accuracy of 
results when age groups of one-half year or one month, 
instead of one year, are taken. Several principles of 
probabilities are stated and applied to the study of popu- 
lation. He inquires into the causes affecting the growth 
of population and classes these as general and fortuitous. 
He shows clearly the advantages of large numbers, and 
especially of averages deduced from a series of such 
numbers extending over several years. Finally he states 
repeatedly that average values depend on general causes, 
and change only very slowly " by the secular progress of 
institutions and customs." 

In the memoir of the second volume of the Recherches 
statistiques should be noted the fourth section, Remarque 
gknkrale sur le degrk de precision des rSstiltats moyens. 

1 Paris, 6 vols.; Fourier's essays are in the volumes for 1821 (2nd ed., 
1833), 1823 (2nd ed., 1834), 1826 and 1829. 

2 Vol. i (1821), pp. ix-lxxiii. 



50 ADOLPHE QUETELET AS STATISTICIAN [ 4 g 2 

The third introductory essay, Memoire sur les resultats 
moye?i$ cfun grand nombre cC observations? presents for- 
mulas for finding the degree of precision 2 and the prob- 
able error of the average. 3 He presents a method of 
finding the quantity which when multiplied by three 
gives the positive and negative limits of error in a group 
of measurements, 4 and when multiplied by .47708 gives 
the probable error, which he calls the average error. 
These results are then generalized in the Second mkmoire 
sur les rhultats moyens et sur les erreurs des mesures, 5 
treating by the use of the calculus the probable error of 
a result derived from any number of values each having 
its own probable error. Quetelet undoubtedly had early 
access to these volumes and was much stimulated by 
them. 6 

Thus the School of Political Arithmetic in contradis- 
tinction from the descriptive school, began by laying 
emphasis on the method of inquiry. Their central ob- 
ject of statistical investigation was the population, and, as 
more abundant data accumulated, they perfected both 
their conclusions and their technique. This is especially 
true of the development of mortality tables, which by 
the close of the eighteenth century had led to consider- 

1 Ibid., vol. iii (1826), pp. ix-xxxi. 

''•Ibid., pp. xv, et seq. and p. xxv. 

3 Ibid., pp. xviii, et seq. 

4 The probability is \\%%% that the true result lies within A (average) 
-f 3g and A — 3g. 

h Ibid., vol. iv (1829), pp. ix-xlviii. 

'Thus Quetelet says in the preface to Instructions populaires sur le 
calcul des probability (Brussels. 1828), that he has made large borrow- 
ings from Laplace and that "lessons 12 and 13 are extracted in great 
part from the excellent introduction to Recherches statistiques sur la 
ville de Paris." He should have included also lesson 14, for it is clearly 
from the same source. 



493] QUETELET IN THE HISTORY OF STATISTICS 5I 

able insight into the nature of statistical data and the 
true method of treating them. Finally in the works of 
Laplace and Fourier we note decided indications of a 
tendency to give direct attention to the problem of tech- 
nique and to extend the application of such technique to 
observations of natural and social phenomena. It was the 
function of Quetelet to gather up these various tenden- 
cies, to perfect the method, to extend the scope of its 
application and to give the whole a new and profound 
significance. His activity may be treated under the 
headings, (I) population statistics, (II) moral statistics, 
(III) development of technique and (IV) application of 
the normal law of error to the physical measurements of 
men. 

(I) The studies in the statistics of population com- 
prised in Quetelet's works 1 may be classed under three 

*The chief studies of population statistics are: 

i . " Memoire sur les lois des naissances et de la mortalite a Bruxelles, ' ' 
presented to the Brussels Academy, April 25, 1825, Nouveaux mimoires 
de V acad. roy. des sci. et bell. -lei. de Bruxelles, vol. iii (1826), pp. 493- 
512. 

2. " Recherches sur la population, les naissances, les deces, les 
prisons, les depots de mendicite, etc., dans les Pays-Bas," presented to 
the Academy, February, 1827, ibid., vol. iv (1827), pp. 115-165. 

3. " Recherches statistiques sur le royaume des Pays-Bas," presented 
to the Academy, December, 1829, ibid., vol. v (1829), pp. vi, 57 and 
tables. 

4. Recherches sur le reproduction et la mortalite* et sur la population 
de la Belgique. Publie avec M. Smits. Premier recueil officiel (Brus- 
sels, 1832). 

5. Sur V homme et le diveloppemeni de ses faculty's, ou essai de phy- 
sique sociale (2 vols., Paris, 1835), book 1. 

6. " De l'infiuence des saisons sur la mortalite aux difrerens ages dans 
la Belgique," Nouv. mim., vol. xi (1838), 30 pp. 

7. " Sur le recensement de la population de Bruxelles," Bulletin de 
la commission centrale de statistique, vol. i (1843), PP- 27-164. 

8. " Nouvelles tables de mortalite pour la Belgique," ibid., vol. iv 
(1851), pp. 1-22. 



5 2 ADOLPHE QUETELET AS STATISTICIAN [ 494 

heading's, (a) studies of births, deaths and marriages, 
(b) treatment of the law of population, and (c) develop- 
ment of tables of mortality and of population. 

The study of births, deaths and marriages had been 
treated in a most thorough-going and extensive manner 
by Sussmilch in his second edition of the Gbttliche 
Ordnung (1,761 and 1762), but, since his time, there had 
accumulated a large quantity of material and there had 
been numerous more or less intensive researches on these 
subjects. 1 Among the most important of these were 
those by Quetelet's Parisian friends De Chateuneuf 2 
Villerme and Fourier. The chief merit of Quetelet is in 
the comprehensiveness of his treatment of various phases 
of births and deaths. The best results of his memoirs 
preceding 1835, together with material gathered from 
many sources are found in the Sur V komme? 

(a) Thus in the study of births he inquires into the 
effect of numerous natural and perturbative causes on 
both sex and fecundity ; he inquires into the ratio of 
male to female births (1) throughout Europe, (2) in free 
and slave populations, (3) in town and country, (4) 
among legitimate and illegitimate births ; he investigates 
the influence of age of parents and of conjugal condition 

9. " Nouvelles tables de population pour la Belgique," ibid., pp. 71-92. 

10. " Sur les tables de mortalite et de population," ibid., vol. v (1853), 
pp. 1-24. 

11. " Statistique Internationale (population) par A. Quetelet et X. 
Heuschling," ibid., vol. x (1866), CXV pp. of text and 406 pp. of 
tables. 

Of these, numbers 3 and 10 might be classed as descriptive of official 
statistics. 

1 For list see references, Sur Vhomme, bk. 1. 

'Von John, op. cit., p. 333 note, says that De Chateuneuf, at the insti- 
gation of his friend Poisson, devoted himself most zealously to statistics. 

r 'Sur Vhomme, bk. 1, chaps, i, ii and iii. 



495] QUETELET IN THE HISTORY OF STATISTICS 53 

on the sex of offspring ; he studies the influence of age 
of parents, of place, of years of abundance and scarcity, 
of years of peace and war, of seasons and of hours of the 
day, on the number of births. All the foregoing being 
classed as natural causes, he studies profession, economic 
condition, morality and political and religious institutions 
as perturbative causes. Similar correlations were made 
for still-births ■ and for deaths. 2 These studies contain 
few conclusions that were new at the time, but because 
of their clearness and comprehensiveness in both material 
and number of correlations, they afforded a striking and 
stimulating indication of the advancement of vital statis- 
tics and were an excellent medium for the spread of such 
knowledge. 

(b) Quetelet's treatment of the law of population 3 
does not deserve lengthy treatment. The distinguishing 
feature about it is the statement that the resistance to 
the growth of population increases, all other things being 
equal, as the square of the rate at which population tends 
to increase. He presents neither data nor course of 
reasoning to support this conclusion nor does he explain 
any of the possibilities lurking in the phrase " all other 
things being equal." The theorem therefore is certainly 
not demonstrated. 

(c) Quetelet's first statistical memoir, 4 giving a table 
of mortality with a distinction of sex, sought to provide 
a reliable basis for life insurance in Brussels. A second 
memoir 5 extended the tables of mortality and of popula- 

l Nouv. mini., vol. iv (1827); SurVhomme, bk. 1, chap. iv. 
2 I6id., bk. 1, chap. iv. 3 Ibid., bk. 2, chap. vii. 

4 Nouv. mhn., vol. iii (1826), pp. 493-512. 
h Nouv. mint., vol. iv (1827). 



54 ADOLPHE QUETELET AS STATISTICIAN [ 49 6 

tion to the southern provinces, while studies of 1832 E 
and 1833 2 gave tables for all Belgium. Quetelet early 
made the distinction of sex and of residence in city or 
country; he also brought out the varying rates of mor- 
tality at different ages, as in the early months cf child- 
hood, at the ages preceding puberty, and at the ages 
twenty-four and thirty, in men. Fie perfected these 
tables on the basis of the registers of death for the five 
years 1841-5. 3 The chief importance of these tables lies 
in their great practical value in his own country. His 
first serious attempt at the treatment of the mathemati- 
cal theory of tables of mortality and of population was in 
the memoirs of 185 1 and 1853. 4 This last memoir is in 
three sections, the first two of which treat these tables 
for a stationary population following very closely Fourier's 
method. He however makes the evident error of confus- 
ing the population at the end of a calendar year with 
that at the end of a year of life. The third section treats 
the subject for any population whatever. He however 
assumes that the births of a calendar year occur simul- 
taneously and that all the generations represented in a 
population at a given time have the same rate of mortal- 
ity whether the population be increasing or decreasing. 
Neither of these assumptions being true he fails to reach 
a general formula. Nevertheless his studies were not 
without value to the general progress of the theory. 5 

1 Recherches stir la reproduction et la morialiti de Vhomme aux diffir- 
ens dges (Brussels, 1832). 

2 Sur V influence des saisons et des dges sur la mortaliii, presented to 
the Academy of Moral and Political Sciences of the Institute of France 
in 1833, reproduced in Sur Vhomme, bk. 1, chap. 5, sec. 5, and elabor- 
ated in Nouv. mhn., vol. xi (1838). 

3 Bull, de la cent. com. de sta., vol. iv (1851), pp. 1-22. 
i Idid., pp. 72-92, and vol. v (1853), pp. 1-24. 

5 See Knapp, Theorie des Bevolkerungs-wechsels . pt. 2, p. 93, et seq.\ 
Block, Traitf de statistique, p. 206, et seq. 



497] Q UETELET IN THE HISTORY OF STATISTICS 55 

(II) In 1826 appeared the first of the Comptes gknkr- 
aux de V administration de la justice criminelle e7i France. 
In these annual reports were enumerated the number 
and kind of crimes and misdemeanors, as well as the sex, 
age, occupation and education of the accused. Quetelet 
uses these reports in his " Recherches statistiques sur le 
royaume des Pays-Bas." l In this he compares the sexes 
as to the kind of crimes, presents the relative number of 
crimes committed against persons and against property 
at each age, and tentatively sets forth the relative degree 
of tendency to crime at each age. 2 Comparing the 
figures for the three years, 1825-1827, he emphasizes the 
" astounding exactitude with which crimes are repro- 
duced." 3 He adds, 

Thus we pass from one year to another with the sad perspec- 
tive of seeing* the same crimes reproduced in the same order 
and calling down the same punishments in the same propor- 
tions. Sad condition of humanity ! The part of prisons, of 
irons and of the scaffold seems fixed for it as much as the 
revenue of the state. We might enumerate in advance how 
many individuals will stain their hands in the blood of their 
fellows, how many will be forgers, how many will be poison- 
ers, almost as we can enumerate in advance the births and 
deaths that should occur.* 

The same year, 1829, A. M. Guerry brought out his 
Statistique compare* de V ktat de V instruction et du 

1 Nouv. mint., vol. v (1829), pp. 25-38; read to the Brussels Academy- 
December 6, 1828. 

2 /did., p. 33. % Ibid., p. 35. 

*Nouv. mim., vol. v, pp. 35 and 36. This quotation shows that Quet- 
elet had reached, in 1828, practically the same position as in the " Re- 
cherches sur le penchant au crime aux differens ages" of 1831, which 
is usually tieated as his first work in moral statistics. There is thus 
good ground for giving to Quetelet priority in this field, instead of to 
Guerry as is usually done. 



5 6 ADOLPHE QUETELET AS STATISTICIAN [ 49 g 

nombre des crimes' 1 in which was sought an estimate 
of the moral level of France by the use of statistical data. 
So also, he and D'lvernois endeavored to compare the 
moral level of different countries by comparing their 
criminal records. Quetelet had made such a comparison 
between France and the Low Countries in his " Re- 
cherches " of 1829, 2 but Guerry and D'lvernois saw no 
especial significance in the constancy of the numbers 
from year to year, while it was precisely this that Quetelet 
emphasized. 3 This constancy of the budget of crimes 
was strikingly brought out in his " Sur le penchant au 
crime aux differens ages.'' 4 Regularity in the number 
of suicides was noted in the Sur Vhomme y and the 
constancy in the number of marriages for each age and 
sex, first shown in this same work, became the principal 
object of his later studies in moral statistics. 

Thus it was that, though Guerry coined the term 
" moral statistics," Quetelet gave it significance. He did 
this in the following ways : 

(a) He emphasized the relation of the statistical regu- 
larities to man's moral freedom. The regularities 
which Arbuthnot, 5 Derham and Sussmilch had found 
to be the surest evidence of a divine order main- 
tained for the good of man, Quetelet elevated to the 

1 Paris, 1829. 

2 Nouv. mem., vol. v, p. 27, et seq. 

s Jealousy seems to have existed between Quetelet and Guerry. The 
former, however, relented and in 1847 used Guerry's term "statistique 
morale," but the latter remained unfriendly to the last. See especially 
"Note" following " Recherches sur le penchant au crime" and note 
in Sur Vhomme, English translation, p. 96, near the end of book third. 

i Nouv. mim., vol. vii (1831), 81 pp. 

5 "An argument for Divine Providence, taken from the constant 
Regularity observed in the Births of both sexes," Phil. Tr., vol. xxvii. 



499] Q UETELET IN THE HISTORY OF STATISTICS 57 

rank of social laws, comparable to the laws of physics. 
He gave a scientific, rather than a theological interpreta- 
tion of the facts and thus threw doubt on man's free will. 
" It seems to me that what relates to the human species, 
considered en masse, is of the order of physical facts." 1 
The possibility of predicting in advance the number and 
kind of crimes weighed heavily, at times, upon Quetelet's 
humanitarian spirit. " This possibility .... must give 
rise to serious reflections, since it concerns the fate of 
several thousand men who are driven, as it were, in an 
irresistible manner toward the tribunals and toward the 
condemnations that await them." 2 The picturesqueness 
of his language and the clearness with which he joined 
the issue, compelled attention and led to wide discussion 
of the true nature of statistical regularities and their 
ethical implications. 

{b) At the same time that Quetelet held his averages 
to be " of the order of physical facts," he held them to 
be dependent on social conditions and therefore to vary 
with time and place. This made possible the study of 
causal relations in social phenomena, for a change in 
social conditions would be followed by a change in the 
averages. Thus, social conditions were made responsible 
for the criminal budget and moral statistics was directly 
connected with social science. The problem then be- 
came that of expressly connecting social evils with 
certain social conditions, and by changing the latter also 
change the former. 

(c) But this study of casual relations requires much 
more critical methods of treatment than a purely descrip- 
tive problem. The basic principles of the method pre- 
sented by Quetelet for this study were derived from the 

1 Nouv. mem., vol. vii, p. 80. ' 2 Ibid., p. 23. 



58 ADOLPHE QUETELET AS STATISTICIAN [500 

theory of probabilities. They were: (a) effects have causes 
and are proportioned to them, and (£) reliable conclusions 
can be deduced from large numbers only. These prin- 
ciples are strikingly like those recognized by Sussmilch, 1 
but no doubt they reached Quetelet by way of French 
mathematicians and astronomers, rather than directly or 
indirectly from the German theologian and statistician. 
From the first of these he derived the principle that 
man's moral and intellectual nature would be shown in 
his actions, and that the true nature of a social state 
would be shown in its products. But the effects of for- 
tuitous circumstances can be avoided, and the results of 
general conditions can be seized, only by considering 
large groups of homogeneous data. 

(III) These principles formed a part of his general de- 
velopment of the methods of statistical inquiry. The 
essential features of this are to be noted later, 2 hence it 
will suffice here to say that, although most of the prin- 
ciples utilized by Quetelet in the development of the 
normal law of error and its use in statistical inquiry had 
been already developed by the students of probabilities 
and in the essays of Fourier, yet it was doubtless the 
writings of Quetelet that led to their general appreciation 
and adoption. This was due to the clearness with which 
he stated the results of mathematical analysis and to the 
wide public which his writings reached. It may be em- 
phasized here, moreover, that it was largely through 
Quetelet's application of the same statistical method to 
anthropology, meteorology, astronomy, medicine and 
social science that arose the conception of statistics as a 
widely applicable method of observation. 

(IV) But there is one feature of the application of this 

1 See pp. 47-48, supra. 2 Chapters iv and v. 



501] QUETELET IN THE HISTORY OF STATISTICS 59 

normal law of error which is distinctly his own, and 
which has been of especial significance both for the 
further perfection of statistical method and for the de- 
velopment of biological science. He likened society to 
a body having as its center of gravity the average man.' 
The determination of the properties of this average man 
would, he thought, give a true picture of the general 
features of the social body. These ideas were first pre- 
sented in " Recherches sur la loi de croissance aux dif- 
ferens ages," 2 in which was presented the average height 
of groups of individuals of each age from birth to 
maturity. It was not, however, until much later that 
the idea of the average man as a type about which all 
men of the same class were grouped in accordance with 
a definite law was expressly developed. 3 The average 
man as a type varies with time and place. 4 Similar con- 
cepts were readily applicable to any plant or animal. 
What was true of the distribution of the heights of men 
might prove to be true of any characteristic of a plant 
or animal; and what was true of the average man might 
prove to be true of the type of a species. Hence the 
possibility of studying the subject of biological variation 
by means of exact numerical measurements. 

The preceding survey of Quetelet's statistical activity 
shows both its broadly inclusive character and its epochal 
importance in the history of the science. It is with good 
reason that Von John declares that " Quetelet's master- 
piece of 1835 . . . is in fact a landmark in the historical. 

1 See chap, iii, infra. 

^Nouv. mitn., vol. vii (1831), 31 pp. 

r ' See chap, iii, infra. 

4 Quetelet was not consistent on this point of the variability of the 
average man. 



60 ADOLPHE QUETELET AS STATISTICIAN [502 

development, not only of political arithmetic, but also of 
the German university statistics." 1 Among the causes 
of this eminent position must be included (1) the abun- 
dance of new data ; (2) Quetelet's close contact with the 
French scholars interested in the theory of probabilities 
and in statistics; and (3) the wide publication of his 
results. 

The abundance of new data was of primary impor- 
tance. It made possible the comprehensive treatment 2 
of vital statistics, including a practical table of mortality 
for Belgium, and it raised questions of criticism of 
sources and of method of treatment. Official documents 
being a chief source, Quetelet exerted upon them a far- 
reaching influence both through his own writings and the 
movement for international comparability represented by 
the Statistical Congresses. He was, in this way, largely 
instrumental in bringing such documents to a character 
mid-way between the purely verbal Achenwall-statistics 
and the purely numerical table statistics, by including with 
the tabular results descriptive and explanatory material. 
He extended the scope of statistical inquiry by adding the 
new field of moral statistics. It was mainly by this addi- 
tion and the results following thereupon that the term 
first used to designate a new discipline in the German 
universities came to have that scientific character sought 
by the school of political arithmetic. Emphasizing the 
connection between social conditions and statistical 
results, he made the fundamental aim of the science of 
statistics the study of the co-existence and sequence of 
social phenomena in correlation with the environing con- 
ditions of social life. 

But he not only gave meaning to statistics as a descrip- 

1 Geschichte, p. 370. - Sur Vho-mme, bk. i. 



503] QUETELET IN THE HISTORY OF STATISTICS 6l 

tive science, he also developed the conception of statistics 
as a method of scientific investigation serving all the sci- 
ences of observation. The law of error, developed by 
astronomers, and the theory of probability, cultivated 
zealously by that group of bright men centering around 
the great Laplace, found in the writings of Quetelet both 
simplification and elaboration and a channel of communi- 
cation to an extensive group of readers. Moreover, this 
method found a new, and, to-day, highly significant ex- 
tension in his studies of physical anthropology. 

Finally should be emphasized the fact that practically 
everything of importance that Quetelet hit upon, he pub- 
lished time and again. The Correspondance math&mat- 
ique et physique, the Nouveaux mkmoires ■, the Bulletins, 
and the Annuaire of the Brussels Academy, the Annu- 
aire of the Observatory, and the Bulletin de la commis- 
sion centrale de statistique, as well as his numerous 
works, furnished a varied means of communication with 
an extensive public. If further means were needed they 
would be found in his voluminous correspondence and in 
his connection with learned societies throughout the 
world. 

Quetelet thus gathered up the chief statistical tenden- 
cies of his time, and contributed, in more or less notable 
degree, to the advancement of each. His genius con- 
sisted not so much in original conceptions as in a keen 
appreciation of the importance of various ideas and the 
great practical sense with which he applied them. 



CHAPTER III 

THE AVERAGE MAN 

Quetelet's name is customarily associated with the 
term average man {homme moyen) and with considera- 
tions on the importance of this homme moyen for a 
statistical study of society. The ideas involved in the 
concept, average man, are central in all of Quetelet's re- 
searches and are critical for an understanding of his writ- 
ings. Apart from the unity derived from the more or 
less general presence of the notion of the average man, 
his writings on population and moral statistics, physical 
anthropology, statistical methods and the social system 
are completely lacking in a unifying principle. G. F. 
Knapp holds that there was no continuous unfolding of 
Quetelet's chief ideas. 1 

No doubt the germ of all he has to say is found in the 
writings preceding the Sur f homme of 1835, ^ ut Quete- 
let himself has indicated the natural development of his 
central thoughts. He says in the preface of Du Systeme 
social that in his first work, Sur V homme, he pre- 
sented the idea of the average man as the mean between 
two limits ; that in the Letters he showed that the aver- 
age man as to height is a type about which the heights 
of other men are grouped according to the law of acci- 

^'Bericht iiber die Schriften Quetelets zur Socialstatistik tmd An- 
thropologic." Hildebrand's Jahrbucher fur Nationalokonomie und 
Statistik, vol. xvii, p. 358. 

62 [504 






5 05] THE AVERAGE MAN 63 

dental causes. " In this new work I show that the law 
of accidental causes is a general law which is applied to 
individuals as well as to peoples and which dominates 
our moral and intellectual qualities as well as our physi- 
cal qualities." There was thus, after 1835, development 
in the concept of the average man and an extension of 
its application as a means of interpreting social pheno- 
mena. 

A brief survey of this development and extension will 
serve to bring out the nature of this concept in its final 
form. The first researches on the qualities of the average 
man dealt with the physical qualities of height and 
weight, which are susceptible of direct measurement. In 
the memoir " Recherches sur la loi de croissance de 
1'homme" 2 he says, 

The man that I consider here is analogous to the center of 
gravity in bodies ; he is the mean about which oscillate the 
social elements ; he is, so to speak, a fictitious being for whom 
all things proceed conformably to the average results obtained 
for society. If we wish to establish the basis of a social me- 
chanics (mScanique sociale) , it is he whom we should consider, 
without stopping to examine particular or anomalous cases. 

Thus the normal law of growth expressed in tabular 
form for each sex gives the average heights of male 
and female Belgians, at each age, from five months pre- 
ceding birth to maturity, at about the ages of twenty- 
five and twenty years, respectively. These tables do not 
show the heights any particular individuals will attain at 
given ages, any more than a mortality table would give 
the time of death of particular persons, but they give 

1 Du Systeme social el des lots qui le rigissenl (Paris, 1848), p. ix. 
2 Nouv. mim., vol. vii. 



64 ADOLPHE QUETELET AS STATISTICIAN [- Q 6 

rather the height of the average man at each age. The 
normal law of growth thus shown applies to the whole 
group of Belgians of either sex, viewed as an aggregate. 
It is the law of growth for the average man, the heights 
given being those about which the heights of all persons 
of given age and sex "oscillate." Just how this oscilla- 
tion takes , place Quetelet does not at this time state. 
■He did state however that studies similar to this on the 
law of growth in height should be made for man's various 
physical, intellectual and moral qualities. 

In the memoir " Recherches sur le penchant au crime 
aux differens ages," 1 he uses the term average man 
(homme moyen) for the first time. " If the average man 
were determined for a nation he would present the type 
of that nation; if he could be determined from the 
ensemble of men, he would present the type of the 
entire human species." He here studies the possi- 
bility and the means of determining the average man 
and hints at the average man as the type of the beautiful. 

The next memoir 2 studies the relation of height to 
weight at each age, but it adds nothing to the general 
notion of the average man. The Sur V homme gives, be- 
sides a reproduction of the preceding studies, much gen- 
eral discussion of the average man 3 but adds little to the 
precision of the concept. But in the article " Sur l'ap- 
preciation des documents statistiques et en particulier 
sur 1'appreciation des moyennes" 4 is developed carefully 
the view of the average man as a type. Here, for the 

x Nouv. mint., vol. vii, p. i of the memoir. 

2 Recherches sur le poids de l'homme aux differens ages, Nouv. rnirn., 
vol. vii. 

3 Especially bk. iv. 

* Bulletin de la com. cent, de stat., vol. ii (1845), pp. 205-287. 



507] THE AVERAGE MAN 65 

first time, he gives exact connotation to the word type 
and shows just how the members of a group oscillate 
about the average. Even in the first memoir x certain of 
the tables showed symmetrical distribution about the 
average, but Quetelet did not comment on the symmetry. 
But in this later article this distribution is his theme. 

Having established his scale of possibility, he begins 
an examination of the manner in which the numbers from 
which an average are deduced are grouped about it. 2 
He first distributes 8192 measurements of the height of 
the same person about the average, seven groups above 
and seven below, according to his scale. This leads to 
the question 

whether there exists in a people a type-man, a man who 
represents this people as to height and in relation to whom all 
the other men of the same nation might be considered as pre- 
senting variations more or less great. The numbers we would 
obtain in measuring these latter would be grouped about the 
average in the same manner as those which we would obtain 
if the same type-man were measured a great many times with 
means more or less clumsy. 3 

A study then of the distribution of the chest measure- 
ments of 5738 Scotch soldiers and of the heights of 
100,000 French conscripts shows a close agreement 
between the actual distribution and that calculated ac- 
cording to his scale. In fact he believes that in the 
latter case he is able to prove fraud by the lack of con- 
tinuity in the actual distribution : a congestion below the 
required height and a scarcity just above it indicate that 
some 2000 have escaped service by reducing their height 

1 " Recherches sur la loi de croissance de l'homme." 
* " Sur 1' appreciation, etc" p. 250. 
3 Ibid., p. 258. 



66 ADOLPHE QUETELET AS STATISTICIAN [508 

two or three centimeters. Thus he finds not only con- 
firmation but a practical use of the conception that there 
is a type-man from which all men are but variations. 

In the Letters 1 - the matter is further elucidated 
with much of the same data. If one should make 1000 
measurements of the chest of the Gladiator, or of a liv- 
ing person, or if 1000 sculptors, working without pre- 
conceived notions, should copy the Gladiator and their 
copies should be measured, each set of measurements 
would be grouped in accordance with the law of possi- 
bility. If we assume' that one would likely as not make 
an error of one inch in measuring the chest of a living 
person, then the chest measurements of the 5738 Scotch 
soldiers are grouped with as much regularity as would 
be the same number of measurements made on one in- 
dividual. " The measurements occur as though the 
chests measured had been modelled from the same type. 
If such were not the case the measurements would not, 
in spite of their imperfections, group themselves with 
the astonishing symmetry which the law of possibility 
assigns them." 2 To the objection that the Scotch 
soldiers represent a selected group, Quetelet replied that 
the accurate verification of the principle is more easy 
when all the men of a nation are taken ; the only effect 
of embracing a larger number is to widen the limits of 
variation. 3 

In similar manner Quetelet then treats the heights of 
100,000 French conscripts. The probable error in this 
case, however, is two inches, and his argument for the 
existence of a type rests on the condition that a very 

^Letters on the Theory of Probabilities, trans, by Downes (London, 
1849), pp. 90-105. 
2 Ibid., p. 93. 3 Ibid., p. 94. 



5 9 ] THE AVERAGE MAN 67 

unskillful person with crude instruments would be liable 
to an error of two inches in measuring a conscript of the 
average height. 

Everything- occurs then as though there existed a type of man 
from whom all other men differ more or less. . . . Every peo- 
ple presents its mean and the different variations from this 
mean in numbers which may be calculated d priori. This 
mean varies among different peoples and sometimes even 
within the limits of the same country, where two peoples of 
different origins may be mixed together. 1 

Thus was presented the definite concept of the average 
man as a biological type, about which the actual men of a 
given group were distributed according to the normal law 
of error, or the law of accidental causes as Quetelet 
called it. This type was always spoken of as due to con- 
stant causes and the variations from it as due to acci- 
dental causes. The next step was to generalize this con- 
cept by extending it to all of man's physical properties 
and to his intellectual and moral qualities, whether with 
reference to the normal state of an individual, or to the 
average man of a nation or of humanity considered at a 
definite period of time, or through all the vicissitudes of 
national and human history. 

This generalization is the theme of the Systeme social. 
This work is divided into three books devoted respec- 
tively to man, societies and humanity. The first two 
books are divided into three sections each, treating re- 
spectively the physical, moral and intellectual qualities, 
while the third considers in a general way the effect of 
progress in knowledge on these various qualities, their 
relations to each other and the limits through which they 

1 Letters, p. 96. 



68 ADOLPHE QUETELET AS STATISTICIAN [$ la 

vary. Probably most of the points made in this work 
had been previously noted by Quetelet, but here they are 
grouped systematically. The aim is to show the universal 
validity of the law of accidental causes. " There is a 
general law which dominates our universe . . . ; it 
gives to everything that breathes an infinite variety." 1 
" Among organized beings all elements vary about an 
average state, and these variations, due to accidental 
causes, occur with such harmony and precision that we 
can, in advance, classify them by number and extent." 2 

Thus the average man, at first somewhat vaguely con- 
ceived as a mean between limits more or less extended, 
was at length definitely conceived as a type. His delinea- 
tion was based on a law derived from the mathematical 
theory of chances but believed to have the widest possible 
realization in the phenomena of organic nature. The 
average man, according to Quetelet, will show the effects 
of the operation of "constant" causes, while the varia- 
tions about him will show the effects of " perturbative " 
or "accidental" causes. Thus we have here not only a 
manner of viewing living things, but a criterion for dis- 
tinguishing that which is typical and general, from that 
which is only individual. 

In the determination of the properties of the average 
man, Quetelet carried on many extensive researches. 
This was in fact the particular aim of most all of his 
statistical studies. From the data of population statis- 
tics he sought to discover the conditions attending the 
birth of the average man, and the time and conditions of 
his death. The law of growth showed the height of the 
average man at each age. 3 This was followed by a mul- 

1 Du Systeme social, p. 16. i Ibid., p. 17. 

* " Recherches sur la loi <ie croissance de l'homme." 



5 1 1 ] THE A VERA GE MAN 69 

titude of studies of men's physical proportions at each 
age culminating in the Anthropomktrie of 1871. Simi- 
lar studies in the development of mental and moral traits 
were those dealing with the products of dramatic talent 1 
and with the propensity to crime. 2 Still other moral 
qualities of the average man were sought in the study of 
foresight, of suicides 3 and of marriages. 4 All of these 
studies have great historical significance. Those in the 
plr sical proportions of men were the precursors of the 
physical measurements of criminals as a means of identi- 
fication, and of the measurement of head forms and other 
bodily parts by physical anthropologists as a means of 
racial discrimination. Especially were they the antece- 
dents of the studies in biological variation which bid fair 
to make of biology a relatively exact science. Quetelet's 
studies of mental trials were the forerunners of studies 
in experimental psychology, which seem destined to lay 
the foundation for a science of education. Finally the 
studies in moral statistics opened the way for the induc- 
tive study of social life. 

Quetelet presented a most important and extensive 
role for the average man. 5 Many scientists, so Quetelet 
thought, would find his properties of the highest useful- 
ness. The physician could thus determine the most use- 
ful remedies and the action to be taken, both in the 
usual case and in the unusual, by comparing his patient 
with the fictitious average. The artist and man of letters 

1 Sur V homme , bk. iii, chap. i. 

2 Especially " Recherches sur le penchant au crime aux differens ages." 
Notiv. mhn., vol. vii. 

3 Sur V homme, bk. iii, chap. ii. 

4 Especially " Statistique morale," Bulletin de la com. cent, de stat., 
vol. iii, and " Sur la statistique morale," Nouv. mSm., vol. xxi. 
5 Sur V homme, bk. iv. 



jo ADOLPHE QUETELET AS STATISTICIAN [ 5I2 

could thus present a most truly representative art and 
literature. The politician could thus more accurately 
play upon the general sentiments and beliefs in the form- 
ation of public opinion. The naturalist by the use of 
the average man could fix racial characteristics and 
demarcations, and determine the extent of any changes 
in racial types from time to time. Finally the social 
scientist, by determining the average man for various 
nations, from year to year, throughout the course of 
national history, would be able to ascertain for nations 
as well as individuals, their laws of birth, growth and 
decay, of equilibrium and motion, — the course followed, 
so to speak, by their centers of gravity. 

There is something fascinating in this conception of 
the average man, while the task of its complete realiza- 
tion is stupendous. It is a statistical conception of the 
universe possessing qualities of poetic and artistic beauty. 
Everything is to be viewed as varying about a normal 
state in a manner to be accurately described by beautiful 
bell-shaped curves of perfect symmetry but of varying 
amplitude. Thus it is that the individual varies about 
his normal self; thus members of a group vary about 
their average ; thus the men of a nation, viewed as indi- 
viduals, vary about the average man of the nation ; thus 
a nation varies about its normal state ; and finally, inas- 
much as the qualities of the average man change from 
time to time and place to place in obedience to general 
causes, to follow the course of the average man in the 
whole series of nations would give us, in Quetelet's view, 
the principles of a social physics, the true mechanics of 
human history. 

One of the early objections made to the conception of 
the average man was that he could not be constructed as 
a composite being; that the attempt to put together 



5 !3] THE AVERAGE MAN y T 

numerous average qualities would result in a monstros- 
ity. Cournot argued that the averages of the bodily pro- 
portions of a group of men would not be consistent with 
one another or with the conditions of viability. 1 

Such objections have often been repeated. But such 
controversy comes to naught. Quetelet himself called 
the average man a " fictitious being" in his first use of 
the term. 3 It would seem then pertinent to remark that 
the conditions of viability for a fictitious being, or the 
general harmony of his parts, can have only a speculative 
interest and value. The result obtained by dividing the 
sum of a series of measurements by their number is 
merely a numerical average and becomes the quality of 
an average man only by a flight of constructive imagina- 
tion. The average height of a group is readily trans- 
posed into the height of the average man of that group, 
but no practical utility is gained by such transposition. 
It may also be stated that the essential thing is adequately 
to represent the group, and, for this purpose, the average 
alone is not sufficient. Significant changes may occur in 

1 Cournot reasoned by analogy. He stated that the averages of the 
sides of a series of right triangles do not give a right triangle; nor are 
the sides, angles and areas of a series of any kind of triangles so con- 
sistent with each other as to form a triangle. In like manner average 
bodily proportions will not fit together so as to make life possible. See 
Exposition de la thiorie des chances et des probabilitis (Paris, 1843), 
pp. 213-214. Quetelet replied to this in Du Systeme social, p. 35, et seq. 
He divided a group of thirty men into three sections in such a way that 
the average heights of all three were the same. He then found that 
other average measurements for the three sections were nearly the same. 
He believed this experiment proved Cournot's criticism invalid. Now 
while Cournot's reasoning by analogy is not convincing, Quetelet's ex- 
periment does not meet the issue. It proves only that the averages of 
the same trait of several homogeneous groups are nearly equal, not that 
the averages of several different traits are mutually harmonious. 

2 See p. 63, supra. 



72 ADOLPHE QUETELET AS STATISTICIAN [-74 

the limits of distribution, or in the standard deviation of 
the group measurements, without affecting the average. 
Moreover, in problems of correlation very great impor- 
tance attaches to the association of group characteristics 
throughout the whole scale of distribution. 

It was one of Quetelet's repeated assertions that the 
average man was the type of perfection in beauty and 
goodness. Believing the race to be intellectually pro- 
gressive, he held the average man to be the most perfect 
intellectually, only for the time being. But believing the 
race to be morally unprogressive, he held the average 
man to represent the type of the absolutely good. The 
systematic presentation of Quetelet's argument on this 
point should begin doubtless with the assumption of 
perfectly normal distribution of every characteristic. 
This he fairly well established in connection with physical 
measurements, and he assumed it with reference to 
mental and moral traits. With respect to physical man 
he then represented nature as an artist making a multi- 
tude of copies of the type-man, a type which, he thought, 
remained ever the same z though actual men might vary 
from it more or less. The type was in his mind directly 
comparable to the true ratio of white and black balls in 
the urn from which chance draws are made, a ratio to be 
indefinitely approached by more numerous draws. Thus 
nature is apparently "striving to produce the type," 2 
but fails only because of the interference of a multitude 
of accidental causes. The type may therefore be con- 
sidered the perfect model. Now the only means of dis- 
covering nature's type is by finding an average from the 

1 See p. 78, et seq., infra. 

"Pearson, Grammar of Science (London, 1900), p. 484, uses a similar 
phrase, " Nature aims at a type, i. e., selects round it. etc.'* 



5 j 5 ] 7'tf£ A VERA GE MAN -3 

measurement of many products of nature's art. Hence 
the average found fairly represents the perfect in phy- 
sical proportions for the time being. 

Just how Quetelet reached the conclusion that the 
average man represents perfection in mental and moral 
traits is not equally clear. It seems however to have 
been reached through manipulation of the phrase "free 
from excess and defect." This phrase he frequently ap- 
plied to the average, the excesses and defects being the 
effects of accidental causes. An excess or defect prop- 
erly denotes quantitatively more or less cf a trait than 
the average. But the average, as shown in the preced- 
ing paragraph, having become in many studies the type 
of the perfect, an excess or defect readily came to desig- 
nate too much or too little of a trait, and thus acquired 
qualitative significance. What he meant by an excess of 
mental ability or morality or health Quetelet nowhere 
clearly states. Nevertheless it seems reasonably clear 
that, in his use of the terms, an " excess " was no better 
qualitatively than a "defect." Thus he could use the 
phrase in the most general manner, and, disregarding 
statistical possibilities, speak of a fictitious average man, 
having a group of perfectly harmonious qualities, "free 
from every excess or defect" and hence the type cf per- 
fection of his time. 1 

It is useless here to discuss what may or may not con- 
stitute a standard of perfection. Such standards are 
prone to vary with individual ideals and with the uses to 
which the qualities considered are to be put. But the 
following considerations may be brought to bear upon 

l Sur Vhornme, bk. iv. chap, i, §3; English translation of same, spe- 
cial preface, p. x; Du Systeme social, p. 28, et seq.; Physique sociale, 
p. 391, et seq. 



74 ADOLPHE QUETELET AS STATISTICIAN [ 5I 6 

Quetelet's position as presented in the two preceding 
paragraphs, (i) With reference to physical proportions 
the average may be made a standard of beauty by pre- 
liminary definition. (2) If, however, we take Quetelet's 
objective standard, namely, the type which nature is 
striving to produce, the average is not the standard of 
perfection. For, contrary to Quetelet's supposition, the 
biological type is changing, with the result that nature 
must be represented as striving to produce not the aver- 
age height, for example, but a height somewhat above 
or below the average — a height more favorable to sur- 
vival and, in this respect also, more perfect. With re- 
spect to the average of mental and moral traits as the 
type of perfection it may be stated, (1) that here, as well 
as in physical traits, the average gives a tolerably perfect 
type of the group but by no means the most perfect in 
the group; (2) that Quetelet seems to have juggled with 
the phrase "free from excess and defect," using it in 
two senses; and (3) that average ability or average 
power in any mental trait is in no danger of being con- 
fused with superior grades of ability or power. If it be 
contended that the perfection of Quetelet's average man 
consisted largely in the harmony and balance of mental 
and moral qualities it could be replied not only that the 
concept of the average man as a composite being having 
been abandoned as of doubtful utility this contention be- 
comes futile, but also that a man combining only average 
qualities would be a mediocre person, without intellectual 
vigor or moral flavor. It might be stated also that 
theoretically the combination of causes provides that a 
large group may include one or more individuals pos- 
sessed of superior grades of abilities, whether physical or 
mental, all as well-proportioned as in the average of the 
group. 



517] THE AVERAGE MAN 75 

It is usual, in criticisms of Quetelet's average man, to 
point out the inconsistency of viewing - him as a type of 
perfection and nevertheless as somehow endowed with a 
propensity to crime. But while such a criticism may 
possibly be apropos, it is an extremely obvious one, and 
one that neither throws any light on the true nature of 
the so-called " propensities " nor advances our compre- 
hension of the nature of Quetelet's efforts. 

The nature of his studies and the true criticism on the 
point raised in the preceding paragraph may be brought 
out by distinguishing the results obtained by different 
statistical inquiries made by Quetelet. In the first place 
he distributed the individuals of certain groups on the 
basis of the normal law for the purpose of finding the 
average height or average weight of the groups. Such 
a group might be the entire population of a country, a 
large group of soldiers, or a large number of persons of 
a given age. The result obtained was the average height 
or weight of the groups studied. Quetelet called such a 
result a quality of the average man, and certainly, if the 
qualities of the average man are to be determined at all, it 
must be by such a process. Quetelet always thought of 
a population group as distributed with reference to every 
trait, physical, mental and moral, in such a way that the 
departures from the average "become rarer as they be- 
come greater, whether above or below, and so that these 
variations, both in number and size, are subject to a law 
which is that of accidental causes." z He did not how- 
ever make such a distribution with reference to any 
mental or moral trait. 2 A second sort of statistical 

1 "' Sur la statistique morale et les principes qui doivent en former la 
base," Nouv. m£m., vol. xxi, p. 10. 

- On the page cited in the preceding reference he suggests such a dis- 



y6 ADOLPHE QUETELET AS STATISTICIAN [ 5I g 

studies was that in which certain kinds of social events, 
as suicides or marriages, occuring in a group viewed col- 
lectively, were counted and the average number for a 
series of years was found. The result was a so-called 
statistical regularity, indicating the probable number of 
similar events that would occur in the same group dur- 
ing the succeeding year. Very similar to these were the 
studies in which Quetelet distributed the number of cer- 
tain moral acts, as crimes, according to the ages of the 
persons committing them. He then divided the number 
of acts by the total number of persons in the respective 
age groups. The results showed the respective prob- 
abilities of committing crime at various ages. These 
probabilities Quetelet called the ''propensity to crime" 
{penchaiit au crime). x If these distinctions be sound, 
it should be evident that the so-called "propensities" to 
crime, to marry, to commit suicide, as Quetelet found 
them, are not characteristics of the average man of the 
group. The average man may have a certain inclination 
to commit crime, but it is not ascertainable from a study 
of the criminal registers. The persons committing 
crime are, with respect to the group average, all on one 

tribution with reference to the tendency to marry, and, on page 14 of 
the same essay, he presents a curve to illustrate the distribution of a 
population with reference to the propensity to crime, or the probability 
of committing crime. The actual distribution, however, is not made. 
Moreover the accompanying discussion shows that his curve actually 
represents the comparative probability of committing crime at each age. 
It does not represent the distribution about the average propensity or 
probability. 

J In the " Recherches sur le penchant au crime aux differens ages," 
Nouv. mim. t vol. vii, p. 17, Quetelet defines the penchant au crime as 
the greater or less probability of committing crime. Moreover in Du 
Systeme social he suggests as a substitute for the word penchant the 
word possibility . 



519] THE AVERAGE MAN yy 

end of the curve of distribution, the other end of the 
curve representing those persons who have an abhorrence 
of crime, or a propensity to conformity to law. Owing 
therefore to the prominence given by Quetelet to the con- 
cept average man, even in the " Recherches sur le pench- 
ant au crime aux differens ages," he may be criticised 
for not indicating just when he did and when he did not 
ascertain a quality of this fictitious being. 

But far more important than the foregoing was Quete- 
let's conception of the average man as a biological type. 
His argument here was very similar to that already pre- 
sented with regard to the average man as the type of 
physical beauty.' It rested on the analogy between the 
distribution about the average and the distribution of 
the accidental errors. As already shown, 2 Quetelet found 
in the symmetrical distribution about the average evi- 
dence that the average was a type which nature was seek- 
ing to produce. Chest measurements of Scotch soldiers 
and heights of French conscripts were distributed in the 
same way that the same number of measurements on one 
person would be distributed, on the assumption that one 
would in the latter case likely as not make errors equal 
to the probable errors of the measurements of chests or 
heights. Thus, the men of a nation were grouped about 
their average "as if they were the results of measure- 
ments made on one and the same person, but with instru- 
ments clumsy enough to justify the size of the varia- 
tions." 3 

Quetelet's analogy between the efforts of nature in 
producing a type and of man in measuring a height of a 
person was in appearance considerably weakened by the 

1 Pp. 72-73 supra. 2 Pp. 65-67 supra. 

8 Du Systhme social, p. 18. 



yg ADOLPHE QUETELET AS STATISTICIAN [520 

fact that an error of three feet eleven inches in measuring 
a height of five feet four inches is extremely improbable. 1 
But Quetelet's comparison may be viewed as an illustration 
of how the distribution of biological measurements in na- 
ture may be expected to occur, not as a proof of nature's 
intentions. Moreover, as Professor Venn has pointed 
out 2 the "ideal" series of chance must be distinguished 
both from the series obtained by measuring a group of 
homogeneous things and from that secured by many 
measurements of the same thing. The first of these is 
arrived at deductively, expressed by the binomial law and 
remains ever the same; the others are arrived at induc- 
tively and vary with conditions. In the case of the third 
alone does the limit represent a real thing which may be 
approached indefinitely by multiplying the number of 
measurements. The type in this case is real and fixed. 
But in the second case the type is fictitious, and in living 
things is changing, with the result that measurements 
continued through a long period of time do not give an 
indefinite approach to the type. 

Quetelet was by no means clear and consistent as to 
the permanence of the type. He usually spoke of the 
average man as varying from country to country, as not 
being the same for urban and for rural populations, as, 
in fact, being different in different environmental and 
social conditions. 3 In other words, "the average man 
is always such as is comformable to and necessitated by 
time and place." 4 In direct contradiction to these ideas 

1 He found the average height of Frenchmen to be five feet four 
inches, and the extremes, seventeen inches and nine feet three inches. 
2 Logic of Chance (3rd ed., London, 1888), p. 26, et seq. 
3 Letters, p. 96; Du Systhne social, p. 14, et seq. 
* Sur I'homme, bk. iv, chap, i, § 3; or, Physique sociale, vol. ii, p. 391. 



^2l] THE AVERAGE MAN yg 

he stated as his belief that the average physical proper- 
ties of man have not varied from the earliest times. 1 He 
held that plants and animals, subject to the immutable 
laws of nature, have ever "an unalterable type." " The 
tree type has remained the same" for the olive since the 
days of Codrus ; even to the size and number of leaves it 
has not changed. 2 Among plants and animals not only 
has the average, according to Quetelet, remained the 
same, but the limits through which variations occur have 
likewise remained unchanged. 3 He then introduces still 
greater confusion by the apparently contradictory state- 
ment that man has been able not only to raise his aver- 
ages but also to restrict the limits of variation, through 
the acquisitions of science. 4 

It seems impossible to reconcile these various proposi- 
tions. It is clear from the examples he gives that the 
last statement does not imply in any way a conscious 
application of laws of inheritance and biological selection, 
but merely the effect of the advance of such sciences as 
optics and surgery in reducing physical defects, and the 
effect of the spread of knowledge in reducing illiteracy 
and in raising the average intelligence. As regards 
changes in the human type, therefore, either in the 
type itself or the limits of variation about it, the ac- 
quisitions of science which Quetelet had in mind, are 
in all probability ineffective, their effectiveness being de- 
pendent upon the extremely doubtful tenet that acquired 
characteristics are inherited. A partial reconciliation of 
the other statements of Quetelet regarding the perma- 

1 Du Systhne social, pp. 252 and 257; Physique sociale, vol. ii, p. 392. 
2 JDu Systeme social, pp. 252 and 257, et seq. 3 Ibid. 

4 Ibid., p. 259; see also Sur Vhomme, bk. iv, chap, i, § 3, or Physique 
sociale, vol. ii, p. 396. 



go ADOLPHE QUETELET AS STATISTICIAN [- 22 

nence of the type may be found in his division of causes 
into natural and perturbative. He says, 

The average height of man is an element which has nothing- 
accidental about it ; it is the product of fixed causes which 
assign to it a determined value. 1 . . . Professions, wealth, 
climate may cause the development of height among different 
peoples to vary. Nature and man work together to produce 
these modifications. I have distinguished these two kinds of 
action by the names of 7iahiral and perturbative forces. The 
first have a character of fixity and permanence vhich does not 
pertain to the second. The latter work as do accidental 
causes. 2 

Thus, assuming unchanging physical conditions, an un- 
changing average height would result, while different 
groups within the same physical environment, selected 
on the basis of occupations, for example, might have dif- 
ferent average heights. So much may be said by way of 
reconciliation, keeping in mind the analogy of drawing 
balls from a bowl which served Quetelet as an epitome 
of nature. 

But even this falls short of being satisfactory. If 
"perturbative" cause act as do accidental causes, then 
they should not be linked with " natural " causes to ex- 
plain the difference in the average height of two peoples. 
If man's action is only " perturbative," and therefore 
accidental, it could not change the average. But it is 
interesting to note how very close Quetelet came to the 
discovery of the selective action of environment. He 
was only one step from it in his proposition that the 
average conforms to the necessities of time and place. 
This statement strongly suggests modification through 

1 Du Systems social, p. 17. 3 Ibid., p. 21, et seq. 



523] THE AVERAGE MAN 8l 

change of environment and adjustment to environment. 
But Quetelet posits unchanged physical conditions 
throughout recent geologic time 1 and apparently over- 
looks the possibility of the migration of a species from 
one environment to another. 

There are other passages in Quetelet which likewise 
suggest a selective process in nature. These are the 
passages dealing with asymmetrical distribution, or 
cases "when the chances are unequal." He found an 
exception to the general rule of symmetry in the distri- 
bution of weights. His limits here were 19 livres and 
649 livres, with an average of 140 livres. These limits 
differ from the average in the ratio of one to four. 2 But 
Quetelet passes over this exception to his general rule 
by insisting that the distribution is continuous and that 
the numbers of individuals above and below the average 
are the same. In the Letters 3 he finds similar sets of 
observations in the daily fluctuations of temperature in 
winter, changes in the prices of grain, variation in the 
mortality rate, and the ratio of the sexes at birth, while 
barometric pressures extend farther below than above the 
average. He concludes that " Nature is like man in this 
— when it differs from its type, it is more often in exag- 
geration than in diminution." 4 This is evidence, he 
says, that the causes tending to produce variation in one 
direction are stronger or more numerous than those 
operating in the opposite direction. His illustrative 
explanation of the condition in nature which the unsym- 
metrical curve represents is based on the distribution of 
chances in drawing balls from a bowl in which the white 
and black balls are not equal but in the ratio of three to 

1 £>u Systeme social, p. 257. 2 Ibid., pp. 44-45. 

■" Letters xxv and xxvi." 4 Du Systtme social, p. 113. 



8 2 ADOLPHE QUETELET AS STATISTICIAN [524 

two. 1 But Quetelet undoubtedly thought of the ratio 
in nature as "determined and immutable." 2 Thus, 
though he used many expressions suggestive of evolu- 
tionary change of the type, he did not grasp the notion 
of such change. 3 Though he developed and used the 
method which has come to serve in the work of Galton, 
Pearson and others as the basis for the mathematical 
demonstration of evolutionary development, he did not 
himself make any such use of it. 

1 Du Systeme social, p. 118, et sea. 2 Ibid., p. 118. 

3 This does not overlook those passages in which he speaks of the 
progressive development of man's intellectual faculties. In these he 
refers not to any biological change, but only to the increase in man's 
command over nature through the growth of scientific knowledge. 



CHAPTER IV 

MORAL STATISTICS 

It has already been stated that Quetelet's studies in 
moral statistics opened a new field to statistical research, 
the sphere of human actions, where all is apparently in- 
determinate and individual. His venture into this field 
created very wide discussion, especially in Germany, fur- 
nished a statistical basis for some of the generalizations 
in the early pages of Buckle's History of Civilization in 
England, and was significant in the development of the 
methods, concepts and scope of statistics. The purpose 
of this chapter is to survey the principles and methods 
of moral statistics as Quetelet presented them. 

By moral statistics is meant that portion of the general 
science dealing with such individual actions as are com- 
monly classed as moral or immoral. The phenomena 
usually dealt with are crimes, suicides and marriages. 
These actions have the characteristics of occurring more 
or less frequently in a social group, of giving opportu- 
nity for the exercise of individual discretion, judgment, 
will, and of being correlated quite directly with social 
conditions. Any similar acts would supply data for 
moral statistics. The first aim is to establish the norms 
for various kinds of moral actions, that is, the average 
number that occur under given conditions during a 
period of time. These norms form the statistical regu- 
larities, for it is found that in a series of years the 
numbers of crimes, suicides or marriages vary about 
525] 83 



84 ADOLPHE QUETELET AS STATISTICIAN [526 

their average, showing a tendency for the average num- 
ber to be repeated from year to year. These regularities 
are often called statistical or sociological laws. Moral 
statistics then attempts to correlate the phenomena under 
investigation with certain physical and social conditions, 
by showing variations in the numbers as the conditions 
are changed. To do these things it follows certain well- 
defined canons and methods. The following pages will 
present briefly Quetelet's work and conclusions in this 
field, and will consider the nature and value of statistical 
regularities and the principles of the method followed. 

In the " Recherches staiistiques surle Royaume de Pays- 
Bas," 1 Quetelet makes his first study in moral statistics. 
Aside from the comparisons of France and the Low 
Countries he studies the ratio of condemned to accused, 
the distribution of crimes by the age and sex of the per- 
petrators, and the number of crimes against persons and 
against property committed by the persons of each age 
group. This last matter is presented in a table, there 
being twelve age groups between those under sixteen and 
those over eighty. In this he gives for the first time a scale 
of the penchant au crime for the various age groups, 
that is, the ratio between the number of persons and the 
number of crimes for each group. He then compares the 
numbers for three years under various aspects, emphasiz- 
ing the remarkable uniformity of the numbers from one 
year to another. 2 

The " Recherches sur le penchant au crime aux diffkr- 
ens dges" 3 is easily Quetelet's most comprehensive study 
of crimes. It contains sections on the penchant au crime 

l Notiv. mim., vol. v, pp. 25-38. 

2 See quotation, chap. II, p. 55, supra. 

3 Nouv. mim., vol. vii. 88 pages. 



^ 2 J'\ MORAL STATISTICS 85 

in general, and on the influence of education, climate, 
seasons, sex and age on this propensity. The distinction 
of crimes against persons and against property is preserved 
throughout. At this point we wish to note only his 
emphasis on the constancy of the numbers from year to 
year. He places as much confidence in his scale of pro- 
pensity to crime as in his scale of stature or of mortal- 
ity. 1 After pointing out that murders often follow quar- 
rels and other apparently fortuitous encounters, he says, 
"Nevertheless experience has proven, that not only mur- 
ders are annually almost in the same number, but even 
the instruments which are used to commit them are em- 
ployed in the same proportions. . . Thus . . . we pass, 
etc., 2 as quoted in chapter II, p. 55. And he closes with 
the famous sentence, "There is a budget which we pay 
with a frightful regularity ; it is that of prisons, chains and 
the scaffold. " 3 

The Sur V homme of 1835 added to the preceding essay 
a chapter on suicides and duels in the characteristic man- 
ner, and several brief articles of 1835 and 1836 in the 
Bulletins de V acadkmie royale de Bruxelles* were de- 
voted partly to general considerations on the freedom of 
the will and the regularity of certain social phenomena. 
So great does he find the constancy in the number of 
marriages by age groups that in the essay of 184.7 ne * s 
able to present a scale of the propensity to marry, 5 and 
similarly in the essay of 1848 he calculates a scale for 

1 Op. cit., p. 71; also English trans, of Sur V homme, p. viii. 

2 Ibid., p. 79. z Ibid., p. 81. 

* " Sur Ies maladies des conscrits en France," vol. ii (1835), pp. 277- 
279; "Sur la justice criminelle en Belgique," ibid., pp. 360-372: and 
" De 1'influence de l'age sur l'alienation mentale et sur le penchant au 
crime," vol. iii (1836), pp. 180 and 210. 

5 " Statistique morale," Bulletin de la com. cent, de slat., vol. iii 
(1847), especially note pp. 140 and 141. 



S6 ADOLPHE QUETELET AS STATISTICIAN [ 52 g 

suicides. 1 In these later studies he repeatedly emphasizes 
the impressive regularity in the figures from year to year. 2 

It was this emphasis upon the constancy of the social 
" budgets" which brought upon Quetelet the charge of 
being a fatalist and a materialist. It was this also which 
called forth the widest discussion and an abundant liter- 
ature on the meaning and implications of the regularities 
revealed by moral statistics. 3 Quetelet's explanation of 
this constancy is therefore not without interest. He has 
nowhere given a formal and thorough discussion of this 
question, hence it will be necessary to bring together 
some of his most pertinent ideas. 

Quetelet held quite consistently to the proposition that 
there is no such thing as a real chance occurrence, that 
is, there is no such thing as an uncaused or unrelated 
event. 4 If events have causes, and the same causes per- 
sist from one period of time to another, then the same 
events may be expected to reoccur. This principle 
received its first expression in the Recherches statistiqties 
of 1829 in the form, "The same causes persisting we 
ought to expect the same effects to be reproduced." 5 
"The laws presiding over the development of man, and 
modifying his actions are in general the result of his or- 
ganization, of his education or knowledge, means or 
wealth, institutions, local influences and an endless variety 

l " Sur la statistique morale." Nouv. mim., vol. xxi, p. 36. 

2 See particularly " Statistique morale," p. 143, et seq., where he speaks 
of the number of marriages as another "budget controlled by the cus- 
toms and the needs of our social organization." 

8 See Von John, Geschichte der Statistik (Stuttgart, 1884), pp. 362, 
et seq.; for a summary of views of many writers on this subject see 
Block, TraitS statistique, pp. 137, et seq. 

*See chap, i, p. 18, supra. 

5 Page v, and repeated many times, especially English trans, of Sur 
Vhomme, p. vii and p. 6. 



5 2o] MORAL STATISTICS 87 

of causes . . ." * Quetelet lays much stress on the in- 
fluence of physical environment 2 and of social conditions 
and institutions. Man not only possesses individuality, 
he is also a member of society. " From this point of 
view, the regularity which we note in the formation of 
marriages ought to be attributed not to the volition of 
individuals, but to the habits of this concrete being which 
we call a people, and which we regard as endowed with 
a volition of its own and with habits from which it frees 
itself with difficulty." 3 "Moral causes which leave their 
traces in social phenomena are then inherent in the nation 
and not in the individual." 4 Variations in the marriage 
statistics of different provinces are due " to moral causes 
which exist outside of the individual and which are pecu- 
liar to each people. These moral causes have not essen- 
tially a character of fixity, as have causes in nature, but 
they fluctuate and vary with time." 5 

It seems to me that that which relates to the human species, 
co7isidered en masse, is of the order of physical facts ; the greater 
the number of individuals the more the individual will is 
effaced and leaves predominating the series of general facts 
which depend on the general causes, in accordance with which 

l Ibid., p. 7; first stated in " Recherches sur la loi de croissance de 
l'homme," Nonv. mfrn., vol. vii, p. 1 of the essay. 

2 Du Systeme social, p. 8. 

3 " Statistique morale," p. 142. 

4 " Sur la statistique morale/' Nouv. mim., vol. xxi, p. 6. In " Statis- 
tique morale," p. 138, he says, "All occurs as if a people had intended 
to contract annually almost the same number of marriages and to divide 
them in the same proportions among the different provinces, between 
city and country, and between bachelors, maidens, widowers and 
widows." 

5 " Statistique morale," p. 142; in Sur l'homme, § 2, he says, "The 
laws which relate to the social body are not essentially invariable; they 
change with the nature of the causes producing them." 



88 ADOLPHE QUETELET AS STATISTICIAN [530 

society exists and maintar'ns itself. These are the causes we 
seek to ascertain, and, when we shall know them, we shall de- 
termine effects for society as we determine effects by causes 
in the physical sciences. l 

This last quotation contains the gist of Quetelet's ex- 
planation. General social conditions influencing the 
greater part of the social group, result in tolerably con- 
stant social phenomena, because, according to the law of 
large numbers, the effects of general causes gradually 
prevail amidst the multitude of variations due to minute 
causes. 

Several consequences followed, in Quetelet's view, from 
these principles. In the first place, if the general social 
conditions act upon man in such an apparently irresisti- 
ble manner when a social group is observed, then society 
as a whole must be made responsible for the moral 
" budgets " due to social conditions. 

The crimes which are annually committed seem to be a nec- 
essary result of our social organization. . . . Society prepares 
the crime and the guilty is only the instrument by which it is 
accomplished. Hence, it happens that the unfortunate person 
who loses his head upon the scaffold, or who ends his life in 
prison, is in some manner an expiatory victim for society. His 
crime is the result of the circumstances in which he finds him- 
self, and the severity of his punishment is perhaps another 
result of it. 2 

A second consequence is that the sphere of individual 
freedom is very narrowly limited. Ouetelet seems some- 

1 " Recherches sur le penchant au crime," pp. 80-81 of the essay; see 
also " Recherches sur le poids de l'homme," p. 10. 

2 Sur Vlwmme, last section; English trans., p. 108; see also p. 6 of the 
translation. 



-3 1 ] MORAL STATISTICS 89 

times wholly to deny the existence of free will, but, as a 
rule, he speaks of it as a capricious element acting within 
a narrow circle of possibilities. 1 In this view man's will 
is capable of producing the infinite variety found in indi- 
vidual action, but cannot upset the rules of the social 
organization. The individual becomes an accidental 
cause, and its effects mere accidentalities ; hence, when a 
social group is viewed, these effects are neutralized in 
the same manner that accidental errors are eliminated in 
making a series of measurements. 

Charged with being a fatalist Quetelet answered by 
asserting a positive conviction that man can ameliorate 
his own condition by his own efforts. 2 We have seen 
that he believed the "moral causes which leave their 
traces in social phenomena " to be capable of change. 3 
Such changes are, in his view, to be brought about 
through the action of " moral forces " exercised by man 
in modifying the conditions in which he lives. 4 But these 
" moral forces" are perturbative in their manner of action 
and the changes they bring about are very slow, like the 
secular changes in the solar system : for this reason the 
"moral causes" which predominate in the social system 
cannot undergo any sudden change. 5 This perturbative 
action of man, according to Quetelet, depends upon the 
exercise of his reason and increases with the growth of 

l Sur Vhomme, Eng. trans., p. vii; ibid., " Introductory," § 2, p. 6; 
Du Systeme social, pp. ix, 8, 9, 65, passim; " Statistique morale," p. 
136; " Sur la statistique morale," pp. 6, 22 and 35, et seq. 

2 " Recherches statistiques " (1829), note, p. 25; English trans, of Sur 
Vhomme, p. vii. 

3 Supra, p. 87. 

*" Recherches sur la loi de croissance," pp. 1 and 2, and " Recher- 
ches sur le penchant au crime," pp. 2 and 80. 
b " Recherches sur le penchant, etc." p. 80. 



go ADOLPHE QUETELET AS STATISTICIAN [532 

knowledge. 1 The causes over which man has some con- 
trol are the social institutions; and since the modifica- 
tion of effects must begin with the modification of causes, 
the betterment of results must begin with a reform of 
social institutions. 2 In order that this reform may be 
carried out with wisdom and intelligence, it should be 
the part of the statistician, thought Quetelet, to make 
known, so far as possible, the social effects traceable to 
special institutions, and the part of the legislator, in the 
light of this knowledge, to ameliorate social conditions. 3 

The preceding paragraphs make more or less clear 
Quetelet's explanation of statistical regularities, his de- 
liverances on the question of social responsibility for 
crime, and his hope for a positive progress as man grows 
in scientific knowledge. Is his position satisfactory? 

Attempted explanation of the regularities of moral 
statistics has been the cause of much fruitless discussion, 
because attention has been centered upon the implica- 
tions that may or may not be drawn with reference to 
the freedom of the human will. We may avoid this 
barren philosophical discussion by starting from a prin- 
ciple which makes it impossible and by limiting ourselves 
strictly to the field of scientific inquiry. It does not 
seem possible for any science to take any other attitude 
toward the phenomena with which it deals, than that 
they are related in direct and complete continuity with 

1 " Recherches sur la loi de croissance," p. 2. 

2 " De Finfluence de Fage sur Falienation mentale et sur le penchant 
au crime," Bull, de I'acad., 1st Series, vol. iii, p. 185. 

* Sur Vhomme, bk. iv, final section; Eng. trans., p. 108; " Statistique 
morale," p. 146; " Sur la statistique morale," pp. 18-19 an( ^ 3^; "Sur 
la statistique criminelle du Royaume-Uni. de la Grande-Bretagne. 
Lettre a M. Porter, a Londres, par M. A. Quetelet," Bull. cent, com^ 
de sta., vol. iv, p. 121. 



5 33] MORAL STATISTICS gj 

preceding or contemporaneous phenomena. That is, the 
causal explanation of a phenomenon must be found in 
antecedent and coexisting conditions where it arises, 
without resort to some extraneous, unrelated or capri- 
cious element. In so far as a phenomenon is a pure acci- 
dentally it is not material for scientific inquiry. If any 
series or group of phenomena of a pure-chance sort were 
subjected to investigation, no order or relation would be 
discernible among them. Human reason would be use- 
less and powerless in their presence, and inference would 
be impossible. If man's choices were of this sort, psy- 
chology would be forever a futile pursuit and education 
useless and purposeless. To illustrate such a condition 
by the usual figure of drawing balls from a bowl, one 
must conceive a bowl to contain a multitude of balls of 
an equal number of shades of color. 1 The problem to 
be solved would be to ascertain from a finite number of 
draws the probable order of future draws, or the ratio of 
balls of one shade to those of other shades. Even the 
largest conceivable number of draws would give no 
grounds for inference. Under such circumstances we 
must forever remain in the dark with no guide for our 
conduct other than unreasoning fear and superstition. 
The reasoned and ordered knowledge which science 
seeks is possible only under the assumption that the 
efficient causes of events are found in antecedent con- 
ditions. 

This principle of efficient causation must then be ex- 
tended to the sphere of human conduct. This is where 
the rub usually comes. The older view of a self with a 
will extraneous to the motives to action and with a power 

^evons, Principles of Science (London, IQ05), p. 2. refers to Con- 
dorcet's expression, "an infinite lottery." 



g 2 ADOLPHE QUETELET AS STATISTICIAN [-34 

of fiat regardless of the conditions of life has generally 
been discarded. But many, like Quetelet, who give 
great emphasis to the necessities which the conditions of 
life force upon us, still reserve a little circle within which 
this old-time self may disport at pleasure, and exercise 
its will without let or hindrance. According to the view 
which we present as the only basis for scientific inquiry, 
even this little circle and the self, independent of char- 
acter, motives and conditions, must be given up. This 
is a completely and frankly deterministic basis. It still 
preserves that conception of free will which means ability 
to act in accordance with our own character and motives 
—the sort of freedom of which all are conscious. More- 
over, when it is once seen that scientific knowledge is de- 
pendent on their being an order in man's world, and 
that true freedom for man is dependent upon the acquisi- 
tion of a knowledge of that order, it may be added that 
the deterministic basis makes possible the only freedom 
that is worth while or even possible for rational creatures. 
It seems perfectly sound then to find the explanation 
of statistical regularities in the persistence of causes. 
Were we in imagination to reduce society to a state akin 
to the static state of the economist, in which the in- 
ternal and external conditions obtaining throughout the 
population were exactly duplicated from one year to the 
next, we should not be astonished at the repetition with 
a dull monotony of the whole gamut of social budgets. 
But in actual dynamic society, conditions change slowly. 
Certainly the physical environment does not greatly vary 
from one year to the next ; the physical qualities and the 
mental traits of the population, and its distribution by 
age groups, change little in two succeeding years; the 
social institutions, the customs and beliefs, and knowledge 
likewise change little. Hence the approximate repetition 



53 5] MORAL STATISTICS 93 

of the numbers of social events from year to year. There 
will be, for example, about the same number of persons 
in the population, who by hereditary qualities and experi- 
ence, are capable of committing murder under certain in- 
centives. From one year to another about the same 
number of persons thus prepared meet the needed incen- 
tives, and the deeds are done. Similarly with the number 
of suicides, or births or marriages. The explanation is 
at bottom not different from that of the recurrence of 
approximately the same number of deaths from year to 
year. 

How then shall the fluctuations in the numbers from 
year to year be explained? Quetelet seemed to think 
that these fluctuations were the effects of man's free 
will. 1 For this reason the average of the numbers for 
several years shows the effect of general causes, to the 
exclusion of free will, even, as the true ratio of the balls 
in the bowl is approached as the number of draws is in- 
creased. This however must be viewed as an erroneous 
explanation of the fluctuations. It seems to assume that 
the causes are perfectly constant, but that the number of 
persons who capriciously willed to yield or not to yield 
to their influence varied. But if the tolerable constancy 
of results is explained by a tolerable persistence of causes, 
then the fluctuations must similarly be explained by 
variations in the causes. The number of causes is ex- 
tremely large, and the fluctuations in the results are due 
to differences either in the intensities or in the combi- 

1 This seems to have been the view also of Prof. Richmond Mayo- 
Smith. He says, " With all the regularities there are numerous irregu- 
larities which leave room for the freedom of the individual. And it is 
scarcely possible that statistics will ever be so perfect an instrument of 
investigation as to destroy these variations." Statistics and Sociology 
(New York, 1895). p. 27. 



94 ADOLPHE QUETELET AS STATISTICIAN [536 

nations of the causes. Moreover these variations in the 
causes, instead of being an evidence of man's free will, are 
for the most part entirely, as yet, beyond his control. 
Biological variations in the structure of brain and ner- 
vous system, some unknown element in ancestral hered- 
ity, may be partially responsible for fluctuations in the 
rate of suicide; or a crop failure may account for an 
increase in crimes against property. The point is simply 
that we cannot assume a causal explanation with respect 
to the regularities and a fantastic free-will explanation 
with respect to the fluctuations. 

This holds true also of the variations about the mean 
were the population distributed with respect to some 
moral trait, as tendency to crime. 1 Such a distribution 
would be more or less well represented by the normal 
law of error, the variations running through all degrees 
from abhorrence of crime to a keen delight in it. Such a 
distribution would thus approximate the distribution of 
chances. Does this not indicate that there is some 
purely chance or free-will element which makes it neces- 
sary to provide for more or less extensive deviations 
from the type form? The deviations undoubtedly exist 
but they are not due to some capricious element assumed 
to exist in each person. The deviations indicate a free- 
dom on the part of each person in the group to act in 

1 We may recall here a distinction made in the preceding chapter 
between those statistical studies which ascertain the so-called social bud- 
gets, and those which distribute the members of a social group with 
respect to some trait, the distribution being assumed usually to be nor- 
mal. In the preceding paragraph the fluctuations from year to year, 
found by the former kind of studies, were considered. In this para- 
graph the variations represented by the law of error are considered. 
Quetelet suggested such a distribution as this for mental and moral 
traits, but did not actually make any such distribution. See chap, iii, 
PP. 75-76, st/pra. 



5 37] MORAL STATISTICS 95 

agreement with his character and motives, but even as 
the location of each chance in a scale of chances is de- 
termined by a possible combination of causes, so the 
location of each person in the scale of distribution is de- 
termined by that combination of causes which has de- 
termined his character and motives. What that combi- 
nation is in any particular case may be inscrutable, with 
the result that particular actions are as unpredictable as 
the result of a chance draw. But the word chance in 
this case differs from what we have called pure or abso- 
lute chance, in that it is merely a blanket term for our 
ignorance of and inability to weigh the many minute 
causes which determine the result. So the variations of 
the members of a group about their mean, and the loca- 
tion of every member in the scale of distribution are de- 
termined by the inscrutable and almost infinitely variable 
differences in heredity and environment. The differences 
in natural abilities, in experience, training, education, 
beliefs, are sufficient to explain, in the scientific sense, 
the variations about the mode or the mean. 

Tt has often been stated by writers on this subject that 
the statistical regularities have no compelling power 
over the individual. 1 Recall at this point the manner in 
which the regularity is formed. It is formed by count- 
ing the repetitions of a particular moral act during equal 
periods of time in a population group. The number of 
suicides in the United States in a series of years would 
constitute such a regularity. Now what can be meant 
by the statement that the regularity exerts no com- 
pulsion over the individual, that the individual is free but 
the mass is not, that the rule exists, but the individual 
may or may not follow it? From the point of view 

*See, for example, Majro-Smith, op. cit., p. 27. 



9 6 adolphe quetelet AS STATISTICIAN [-33 

adopted in this essay the only possible interpretation is 
that, whereas there is a high degree of probability that 
the group as a whole will show about the same number 
of suicides during the year following, it is impossible to 
say what particular individuals will do the deeds. But 
this is due merely to our ignorance of the causes 1 oper- 
ating in particular cases. The regularity of moral sta- 
tistics is in this respect similar to the figures of a 
mortality table, as has often been pointed out. The in- 
ability to predict the death of a given person from the 
data of a mortality table is no evidence that this person 
willed not to die at any particular time we might set. 
The conditions of life and character determine whether 
this or that individual shall be numbered among the 
suicides. Moreover, from the manner in which the 
statistical regularity is formed it is evident that the per- 
sons contributing to the so-called budget in any year 
are a small, and, in many cases, a selected group. They 
are found at one extreme of the curve representing the 
whole social group. They show the results of particular 
combinations of causes. The persons represented by the 
other slope of the curve are in no danger of becoming 
suicides ; their conditions of nature and nurture prevent 
such a result. It would seem then that the statement that 
the regularity of the mass exerts no compelling power 
over the individual is at least unenlightening. It is only a 
truism or corollary from the method of rinding the regu- 
larity. A more accurate description is given by the 
statement that the same causes which produce the regu- 
larities do, through differences in their intensity or their 

1 By causes as used throughout this essay is meant simply the ante- 
cedent conditions of an act, that is, inherited structure and the im- 
presses of past experience. 



5 39] MORAL STATISTICS gy 

combination, determine the course of the individual ; but 
that only a very small part of the group is subject to 
those particular combinations of causes, whose effects 
appear in the regularities. If the statement in question 
should be interpreted to mean that the individual is not 
subject to the general conditions of the life of the group 
in which he lives, then we may invoke the whole body 
of social science to show that it is distinctly not true. 

It is usually assumed as a corollary of the statement 
considered in the preceding paragraph that the demon- 
stration of the regularities does not disprove the doctrine 
of free will. This is true if by free will is meant action in 
agreement with our character and motives, but not true 
if a capricious element is meant. As already stated, if 
we explain the regularities by constancy of causes, it is at 
least inconsistent not to explain the variations by changes 
in the causes. Furthermore, when it is shown that the 
regularity changes with a change in the conditions, what 
other interpretation is possible, than that human action 
is determined by the conditions of human life? 

Similar to the foregoing is the statement that the doc- 
trine of free will cannot be disproven by statistics. With 
equal facility it might be said, the doctrine can be proved 
or disproved only by statistics. 1 If by this doctrine is 
meant an uncaused cause, a self-originating something 
without an antecedent but with a consequent, though 
having only a small circle of activity, then it is certainly 
true that statistics cannot demonstrate its non-existence. 
For statistics deals only with groups, and it will never be 
able to eliminate one cause of group variation after an- 

1 Quetelet, English translation of Sur Vhomme, § 2, says, in answer 
to his question " Are human actions regulated by fixed laws," " Exper- 
ience alone can with certainty solve a problem which no d priori rea- 
soning could determine;" also Du SysQme social, p. 65. 



9 8 ADOLPHE QUETELET AS STATISTICIAN [ 54 q 

other, and correspondingly reduce the group, until the in- 
dividual is reached. The causes of variation are practically 
innumerable, and to attempt to eliminate them one after 
another to see whether a final capricious and unac- 
counted-for element remains is not only impossible but 
would be unending were it possible. If however the 
doctrine means only that we are able to do this or that 
if we wish to do it, then it is not at all in conflict with 
the explanation of statistical regularities here set forth. 
For this would simply mean that our character and mo- 
tives determine our actions — character and motives being 
themselves products of the past brought into contact 
with present stimuli. 

Are the statistical regularities of such a nature as pro- 
perly to be called social laws ? Quetelet seems to have 
thought that his regularities were social laws comparable 
to the laws of physics. He speaks frequently of the 
social system in such terms as suggest the Systeme du 
monde of the astronomer. After defining the average 
man as analogous to the center of gravity in bodies, he 
says, " If we wish in some way to establish the bases of a 
social mechanics, it is he whom we ought to consider, 
without stopping to examine particular or anomalous 
cases." 1 In the Recherches sur le penchant au crime" 1 he 
states that the average man will undergo modification 
in time. It should then be determined 

whether these modifications are due to nature or ... to cer- 
tain forces, of which man disposes according" to his free 
will. . . The science which would have for its object such a 
study would be a true social mechanics, which, no doubt, would 

Recherches sur la loi de croissance de l'homme," p. 4. 
2 Page 2. See also " Recherches sur le poids de rhomme," pp. 10, 
11 and 12. 



541] MORAL STATISTICS gg 

present laws quite as admirable as the mechanics of physical 
bodies, and would bring- to light principles of conservation 
which might be perhaps only analogous to those which we 
already know. r 

He often repeated the statement that the results ob- 
tained by viewing a large group of men were of the order 
of physical facts. 2 In the Letters 1 ' he says : 

This great body (the social body) subsists by virtue of con- 
servative principles, as does everything which has proceeded 

from the hands of the Almighty When we think 

we have reached the highest point of the scale we find 
laws as fixed as those which govern the heavenly bodies : we 
turn to the phenomena of physics, where the free will of man 
is entirely effaced, so that the work of the Creator may pre- 
dominate without hindrance. The collection of these laws, 
which exist independently of time and of the caprices of man, 
form a separate science, which I have considered myself en- 
titled to name social physics. 

In the first place it is doubtless an exaggeration, or an 
inaccuracy to speak of the regularity itself as a statistical 
or social law. The average number of suicides in Bel- 
gium, for example, merely acquaints us with a social fact. 
Such a fact is itself variable and has only a greater or 
less degree of probability of being repeated in the suc- 
ceeding year. Such a fact however becomes the basis of 
more or less inclusive social laws when relations of co- 
existence and sequence are established between it and 
the conditions in which it arises. The establishment of 
such relations will of course pass through all the stages 

*Page 2. See also " Recherches sur le poids de l'homme," pp. 10, 
ii and 12. 

2 See supra, p. 87. s Page 178. 



IO o ADOLPHE QUETELET AS STATISTICIAN [ 542 

from hypothetical generalization to more or less exact 
quantitative statement. Changes in the fact thus be- 
come clearly and even quantitatively correlated with 
changes in its conditions. But while both the statistical 
fact and the social laws found through its correlations 
have considerable scientific value, when tested by their 
usefulness in prevision, such value is not so great as that 
of many of the laws of astronomy and physics. In the 
case of these latter, inferences have a degree of assurance 
only slightly removed from certainty, owing to the com- 
pleteness of the induction, the permanency and simplicity 
of conditions and the facility with which effects attribu- 
table to a certain condition or to certain conditions may 
be isolated. But in the statistical study of social phe- 
nomena the complexity and variability of conditions and 
the very great difficulty of isolating the effects of par- 
ticular causes give to inferences from established causal 
relations to future events more or less uncertainty. Not 
only do we not know with exactness the influence to be 
attached to each one of the conditions essential to the 
production of a social event but we do not know the 
proportions which will persist among the conditions 
themselves. Thus it may be shown that the marriage 
rate in England tends to vary directly with the amount 
of foreign trade per capita of the population, T but a 
quantitative statement of the degree of change in the 
former following a specified change in the latter can be 
made only with a considerable margin of error. This is 
because the influence of the amount of imports and ex- 
ports (or any other index of industrial activity) on the 
marriage rate cannot be sufficiently isolated from other 

1 A. L. Bowley, Elements of Statistics (2d ed., London, 1902), pp. 
174, et seq. 



543] MORAL STATISTICS ioi 

influences, such as age grouping of the population, 
standards of living and social customs. It is also due to 
the fact that all the conditions determining the marriage 
rate, and consequently the marriage rate itself, change 
more or less rapidly from decade to decade. 

It does not seem probable therefore that social laws 
derived from the study of the regularities of moral sta- 
tistics will ever become sufficiently general to be " inde- 
pendent of time and the caprices of man," as Quetelet 
expected. Even the law of mortality changes slowly 
with succeeding generations. But concrete social phe- 
nomena change from place to place and time to time 
and may come quickly into vogue and as quickly disap- 
pear. Not only are there variations about the average 
result for a series of years but the type itself changes 
with its conditions. Quetelet's hope of arriving at 
statistical laws independent of time and place was based 
apparently on his assumption of constant causes. He 
always spoke of the average as resulting from such 
causes and hence free from the effects of variable and 
accidental causes. But yet he believed man capable of 
bringing about secular changes in the social budgets. 1 
Quetelet however did not reconcile these conflicting 
notions, 2 nor did he anywhere demonstrate the existence 
of a constant cause. Were the types of social phe- 
nomena the results of really constant causes, then their 
true values could be indefinitely approached by more and 
more observations. But the average keeps shifting in 
obedience to the changing conditions of dynamic social 
life. The illustration of drawing balls from a bowl in 

1 See pp. 87 and 89, supra. 

'For the same conflict with reference to the Average Man, see chap, 
iii, p. 78, et seq., supra. 



102 ADOLPHE QUETELET AS STATISTICIAN [ 544 

which are an infinite number of white and black balls in 
a fixed or determined ratio, which may be forever ap- 
proached, is not true to the conditions in society. The 
ratio must be represented as changing slowly. While 
therefore holding to the mechanical nature of social 
causation, which was fundamental in Quetelet's view, the 
problem of discovering or verifying social laws by a 
statistical process must be made immensely more difficult 
than he ordinarily represented it to be. For the want 
of the concept of evolutionary change Quetelet's social 
physics did in fact provide only for a "social statics." 
To this must be added the more difficult sphere of 
"social dynamics." Not only must the statistical regu- 
larity be correlated with certain dominant social condi- 
tions, but the order of changes in the regularities them- 
selves as correlated with developing social life must be 
discovered and epitomized in the form of scientific law. 

The preceding paragraph makes it unnecessary to em- 
phasize a point made much of in Venn's Logic of Chance* 
that, inasmuch as the type in moral statistics is con- 
stantly changing, not only can it not be indefinitely ap- 
proached by long-continued observation, but it may be 
even missed altogether if statistics are collected through 
so long a time that the results arise under different sets 
of circumstances. 

It remains in this chapter to state certain basic prin- 
ciples of procedure followed by Quetelet in the study of 
the moral actions of men. In estimating the physical 
qualities of men; some, as height and weight, may be 
measured directly, while others, as strength, can be ap- 
preciated only by their effects. It is not absurd to say 
that one man is twice as strong as another with respect 

1 Second edition (London, 1876), pp. 15, 16 and 83 to 89. 



545 ] MORAL STATISTICS 10 $ 

to pressure of the hands, if this pressure applied to an 
obstacle produces effects in the ratio of two to one, con- 
ditions being the same for the two men. 1 Similarly in 
the appreciation of man's moral and intellectual traits it 
is necessary to admit as fundamental that " causes are 
proportional to the effects produced by them"* Thus, 
from a study of actions, literary products, or other effects 
which may be attributed to the presence of a particular 
mental or moral trait, there is sought a knowledge of the 
trait itself. This principle was probably derived by 
Quetelet from the principle of probabilities that the ratio 
of white to black balls in an urn is that shown by 
many drawings. Quetelet applied it in the measure- 
ment of certain mental and moral traits at different ages, 
in the same way in which it would be used by the psy- 
chologist in the study of mental traits and abilities. 
This principle is however precisely the same as that which 
must be used by the sociologist in the inductive study 
of "types of mind" and "types of character" of a pop- 
ulation. 3 

The second principle posited by Quetelet is one that 
is essential to all statistical inquiry, namely, that reliable 
results can be obtained only by the study of many rather 
than few individuals. It is the group rather than the in- 
dividual upon which attention must be centered. It is 
only thus that any order or generality can be ascertained 
amidst the apparently chaotic diversity that is so be- 
wildering when the members of a social group are viewed 
singly. Here again we meet with a principle derived 
from the study of probabilities, namely, " that many in- 

lil Recherches sur le penchant au crime/' p. 6. 
3 Ibid., p. 7. " Sur la statistique morale," p. 7. 
'Giddings, Inductive Sociology (New York, 1901), chap. ii. 



IQ 4 ADOLPHE QUETELET AS STATISTICIAN [546 

dependent disturbing causes of small individual effect 
neutralize one another in the mass." 1 To these two 
general principles might be added many particular ones 
derived from Quetelet's discussion of the necessity of 
comparability of data, of the extent to which small diver- 
sities in the data may be neglected when the numbers 
are large, and of the incompleteness of the records of 
moral actions." 2 

It is possible to make a number of criticisms of Quet- 
elet's results, both in the study of the development of 
dramatic talent and in the study of the penchant au 
crime by ages. Suffice it to say that he was inclined to 
make an exaggerated use of the second principle noted 
above. He relied too much on mere multiplication of 
instances to overcome divergences in the instances 
themselves. 3 But such criticisms by no means affect the 
validity of the general principles of his procedure. A 
scale of penchant au crime derived from the mere num- 
ber of crimes by age groups, without regard either to the 
differences in the gravity of the crimes or to the varying 
proportions in which different kinds of crime are de- 
tected, 4 would not be thoroughly accurate. But this 
means only that attention must be given to these causes 
of error. To study man's nature from the manifestations 

Rowley, op. cit., p. 263. 

2 See " Recherches sur la Roy. dePays-Bas," pp. 29-30; " Recherches 
sur le penchant au crime," pp. 10 and 17, et seq.; Bull, de Vacad., 
vol. ii, note p. 370; Letters, p. 219, et seq., and especially the first 
pages of " Sur la statistique morale." 

3 That he was not unaware of the error here involved is shown by his 
statements in Sur Vhomme, bk. iii, chap, i, § 3, fourth paragraph. 

4 A larger proportion of crimes of violence are detected and brought 
to justice than of petty thefts. Since therefore crimes of violence, by 
Quetelet's tables, are more numerous at ages 21-25 and 26-30 than at 
others, the scale based on numbers only is unduly large for these groups. 



54 7] MORAL STATISTICS IC >5 

of that nature, to study social conditions by means of 
their products, and to study groups rather than indi- 
viduals in order to neutralize individual peculiarities are 
not only valid but absolutely indispensable in statistical 
research. 

It is thus in Quetelet's studies of the moral actions of 
men that is to be found the basis of the quantitative 
study of social life. The Berlin Academy of Science and 
Naum Reichesberg doubtless exceeded strict accuracy in 
hailing Quetelet as " the founder of a new science,'' 
"social physics," or " sociology." x Sciences pass through 
various stages before they become quantitative. As the 
true pioneer in the field of moral statistics, however, he 
formulated and applied with impressive effectiveness the 
method of research which is especially appropriate in 
sociology and economics. It does not seem at all impos- 
sible that the social sciences may one day approximate 
the exactness of the physical sciences. Quetelet would 
then appear as the most conspicuous among the early 
workers in the field of exact social science, and as the 
first formulator of the quantitative method in the study 
of social phenomena. The demonstration of those regu- 
larities in human actions which evidence the presence of 
law, and the formulation of the method for their dis- 
covery were immense contributions to man's knowledge 
of and power over his world. Though Comte used both 
the words social physics and sociology, he did not suc- 
ceed in formulating a method of investigation. This 
was done by his scorned 2 contemporary, Quetelet. 

1 See chap, i, p. 33, supra. 

a Auguste Comte, Cours de philosophie positive, (4th ed., Paris, 1877), 
vol. iv, p. 15, note. 



CHAPTER V 

STATISTICAL METHOD 

In the preceding chapter it was stated that Quetelet's 
main contributions to social science were his demonstra- 
tions of and insistence upon the regularity and order in 
social phenomena and his formulation of a method for 
discovering this order. The exaltation of statistics into 
an exact instrument of observation was more uniquely 
his service than his contention that there are laws of 
human action and social life. The latter was by no 
means a new doctrine — even the inductive study of sta- 
tistical regularities had been more or less steadily carried 
on since the days of Graunt's Observations. But no one 
before Quetelet saw so clearly as he that the basis of the 
method of observation in the biological and social sciences 
must be founded on a general characteristic of social 
phenomena themselves, namely, their variability about 
type forms. This variability is in fact a very general 
characteristic of all observations in which counting or 
measuring is resorted to. Whether in estimating the 
height of an animate or inanimate object from many 
measurements, or the average height of a group of like 
things, as a group of men, whether we seek the reaction 
time of a single individual or of a group of individuals 
there is found a variation of the results about the average 
or type. Quetelet's conception of the average man was 
based on the doctrine that in all that relates to social 
groups there will be found this variability about the 
106 [548 



549 ] STATISTICAL METHOD 1Q y 

group average. His statistical method therefore became 
a search for averages, for the limits of variation and for 
the manner in which this variation, under ordinary con- 
ditions, would occur. It was his general supposition 
that the distribution about the mean would agree with 
the distribution of probabilities shown by the probability 
curve. The first step in the presentation of his method 
will therefore be an exposition of the derivation of his 
probability scale, and its use in the study of averages 
and deviations. Then we shall pass to Quetelet's classi- 
fication of causes and his methods of locating them. 

On its theoretical side Quetelet's statistical method 
was the outgrowth of an application of certain principles 
of the theory of probabilities to his researches. Such 
application is shown in a general way throughout his 
earlier works in his insistence upon the study of groups, 
or the employment of large numbers of observations, in 
order to allow the effects of accidental causes to neutralize 
themselves; in his statement that "the precision of results 
increases as the square root of the number of observa- 
tions ; " x and in his suggestion of the use of the probable 
error in determining the value of data. 2 But his ideas 
were not given systematic treatment previous to the 
essay Sur V appreciation des documents statistioues, et en 
particulier sur £ appreciation des moyennes? 

In the first part 4 of this essay he classifies causes as 
constant, variable and accidental, and shows by examples 
how to detect their presence and how to eliminate the 

1 Sur I'homme, bk. iv, chap, ii; English translation, p. 105. 

2 Ibid., p. 103. 

5 Bulletin de la commission centrale de statistigue, vol. ii (1845), pp. 
205-286. 

* " Premiere partie. Appreciation generate des causes etde leurs ten- 
dances." 



I0 8 ADOLPHE QUETELET AS STATISTICIAN [550 

effects of periodically variable and of accidental causes. 1 
In the second part 2 he sets for himself the problem of 
determining "the degree of energy and the mode of 
action" of these causes. As introductory to this he in- 
quires into the probability of results under various sup- 
positions. In the first place, 3 he supposes the number 
of chances to be known, and to be rigorously equal to 
each other. The probability of the desired result is then 
expressed by a fraction having as its numerator the num- 
ber of chances favorable to the event, and as its denom- 
inator the total number of chances. Thus, in drawing a 
ball from an urn containing three white and one black 
balls, the probability of drawing a white ball is f. The 
probability of drawing a black ball is i, and the sum of 
these two probabilities is unity, the symbol of certainty. 
If the urn contain an infinite number of white and black 
balls in equal numbers, the probability of drawing a 
white ball is i. In a few draws the ratio of the white to 
the black balls drawn may vary considerably from their 
ratio in the urn, that is, may be now too large and now 
too small, owing to the action of many accidental causes ; 
but in a large number of trials there will be drawn 
almost as many white as black balls. This is due to the 
fact that the true ratio of the balls in the urn acts as a 
constant cause, giving to balls of each color the definite 
probability of one-half. 

Quetelet supposes, secondly, that the number of 
chances is unknown. 4 In this case one knows neither 
the colors of the balls in the urn nor the ratio of balls 

1 See infra, p. 129, et seg. 

3 " Deuxieme partie. Appreciation mathematique des causes et de 
leurs tendances." 
z Ibid., §ii; Letters, p. 7, et seg. i I6id., § iii. 



55 1 ] ST A TISTICAL METHOD 10 g 

of one color to those of another. But by repeated draw- 
ings one can determine both of these unknown facts. 
The precision of the ratios thus found, or their approxi- 
mation to the true ratios, " increases proportionally to 
the square root of the number of trials." 1 "But the 
urn we interrogate is nature." 3 Thus, if one asks what 
is the ratio of male to female births, it is necessary to 
bring together the results for a series of years. The 
number of male births for every one thousand female 
births is found to vary in Belgium, 1834 to 1842 in- 
clusive, from 1055 to 1076, with an average of 1065 to 
1000. This ratio in nature is comparable to the fixed 
ratio of white to black balls in the urn ; and in either 
case the true ratio is approached more and more closely 
as the data increase. 

In the third place Quetelet inquires into the law of 
possibility when the number of chances is limited ; that 
is, when the number of chances is small, how are they 
distributed? If the balls are drawn one at a time from 
an urn containing an equal number of white and black 
balls, it is clear that there are two equal chances, either 
a white or a black ball may be drawn. The two chances 
are divided equally between the two possible results or 
in the ratio of 1:1. If we wish to speak in terms of 
probabilities, instead of chances, we may say that either 
result has a probability of h The sum of the probabilities 
of drawing a white and of drawing a black ball is there- 
fore i + i, or unity. 

Suppose next that from a long record of draws made 
one at a time, we unite the first and second, the third 
and fourth, the fifth and sixth, and so on, and that we 
represent white by a and black by b. The first one of 

1 Ibid., p. 230. 2 See also Letters, p. 10. 



HO ADOLPHE QUETELET AS STATISTICIAN [552 

the two balls drawn may be equally either a or b, and 
likewise the second may be equally a or b. If the first 
be a, the result of adding the second may be either aa 
or ab, and if the first be b, the result of adding the 
second may be either ba or bb. All four of these results, 
aa, ab< ba and bb are equally probable. Since however 
ab and ba are alike in composition, each being composed 
of one white and one black ball, there are in reality only 
three possible combinations, namely two white, one 
white and one black and two black, or aa, ab or ba, and 
bb. Among these three combinations the four chances 
are distributed in the order 1, 2, 1, or in the order of 
the coefficients in the expansion of (a + b) 2 or a 2 -f 
2ab J cb 2 . If now we inquire as to the probability of 
each of the combinations, we note that aa has one out 
of the four equal chances, ab (or ba) two out of the four 
and bb, one out of the four; therefore their respective 
probabilities are i 3 f, I, 1 the sum of which again gives 
unity. The probabilities may be obtained directly by 
expanding (i + |) 2 . 

At the risk of tediousness the demonstration may be 
carried one step further, by supposing the draws to be 
taken in groups of three at a time. To each of the four 
equally likely results obtained by taking them two at a 
time will thus be added a or b. There is thus obtained 
eight equally probable combinations, namely aaa, aab, 
aba, abb, baa, bab, bba and bbb. 2 Out of these eight, 

x In the article "Sur l'appreciation, etc.,'" Quetelet does not touch 
upon the probability of a compound event. But in the Letters (" Let- 
ter vi ") he shows that the probability of a compound event is equal to 
the product of the probabilities of the simple events composing it. Thus 
in the case just noted, the probability of drawing a or b is y 2 \ hence 
the probability of drawing aa, ab, ba or bb is % X x /i or %. 

2 From the preceding note it is clear that the probability of any one 
of these eight combinations is (/^) 3 . 



553 ] STATISTICAL METHOD IIT 

only one contains all white or all black, while three con- 
tain two white and one black, and three contain two 
black and one white. There are thus four different com- 
binations, acta, aab, abb and bbb, and the eight chances 
are distributed among them in the order i, 3, 3, 1, or in 
the order of the coefficients in the expansion of the 
binomial (a -f- b) s . The probabilities of the four com- 
binations are evidently 1, f , f and 1, or the results ob- 
tained by expanding (i + i) 3 , the sum of the probabili- 
ties being here, as always, equal to unity. If taken four 
at a time, there are five different combinations, among 
which are distributed sixteen equal chances in the order 
1, 4, 6, 4, 1 or the coefficients of (a + b) i . Moreover 
the probabilities of the five combinations are -ft, t\, t \, 
tV and tV respectively, or the results given by (i+ i) 4 . 
From these examples it appears that the distribution 
of the chances of the various combinations follows the 
order of the coefficients in the successive powers of the 
binomial expansion, or the series given by the successive 
lines of the arithmetic triangle. 1 There is in every case 
a perfectly symmetrical distribution of chances on either 
side of the most probable combinations. It must not 
however be supposed that the various combinations will, 
in actual experiment, be drawn in the proportions indi- 
cated by theory. Many accidental causes lead to fluctu- 
ations of the experienced distributions about the theo- 
retical distribution ; but in the long run these fluctuations 
are neutralized so that by a sufficient number of draws 
the actual distribution of the frequencies of the combina- 
tions can be made to approach indefinitely the theoretical 
distribution. 2 

x Quetelet presents this triangle {ibid., p. 235, and Letters, p. 60) up 
to the 13th line. See Jevons, Principles of Science (London, 1905), 
p. 182, et seq. 

2 Letters, pp. 35-36. 



II2 ADOLPHE QUETELET AS STATISTICIAN [554 

Quetelet next tests this agreement between theory and 
experience by making 4096 draws, one ball at a time, 
from an urn containing forty white and forty black balls. 1 
Each draw is registered and the ball returned to the urn. 
The results are then studied to determine the proportion 
of black balls in all the possible combinations, when the 
draws are grouped two at a time, three at a time and so 
on up to twelve at a time. He also tests with satis- 
factory results the validity of the principle that the pre- 
cision of results increases as the square root of the num- 
ber of draws. 

In the fourth place Quetelet inquires into the laws of 
possibility (or the scale of the distribution of chances) 
when the number of chances is u?ili?nited. t He states that 

when we interrogate nature, the number of chances is gen- 
erally presented to us as unlimited, that is to say, one must 
conceive that each group which is drawn from the urn may be 
composed of an infinite number of balls, and that, conse- 
quently, the number of groups may be likewise unlimited, and 
may present white and black balls in every imaginable com- 
bination. 

But since the number of trials with which one deals in 
experience is always relatively limited, and since one can 
neither actually conceive nor calculate an infinite series, 
Quetelet believes all practical purposes will be served by 
the probabilities of the 1000 combinations that are pos- 
sible when 999 balls are drawn at once from a bowl con- 
taining a multitude of white and black balls in equal 
numbers. The total number of chances in this case is 
represented by a number composed of more than three 

1 " Sur r appreciation, etc.," 2nd part, §§ vi and vii. 
Ibid., § viii. 



555] STA TISTICAL METHOD 1 T 3 

hundred figures. Since in all these chances there is only 
one of drawing all 999 balls of one color, such a result 
may be viewed as impossible. All the combinations 
having more than 549 balls or fewer than 450 balls of 
one color, whether white or black, have all together 
little more than one chance in one thousand, while all 
those combinations having more than 579 balls or fewer 
than 420 balls of one kind, have scarcely one chance in 
ten million. Hence it is useless to consider the proba- 
bilities of combinations beyond these latter limits. 

Quetelet then presents a table (see Table A on the next 
page) showing the probabilities of drawing each of the 
combinations from the most probable one of 499 white 
and 500 black to the scarcely probable one of 420 white 
and 579 black. 1 Each of these eighty groups is paralleled 
by an equally probable one in which the colors are inter- 
changed. Alongside of the scale showing the probability 
of each combination is a table (Table B) which gives the 
"scale of precision," or the sum of the probabilities be- 
ginning with the most probable group, and a table (Table 
C) giving the relative probability of drawing each group. 
Each combination is ranked, the most probable com- 
bination being rank one. The first twenty-two ranks of 
this scale are presented herewith. 2 

1 " Sur l'appreciation, etc.," pp. 244-245. 

2 For the complete table see Letters pp. 256-258; Bowley, op. cit., p. 
273 gives Table B and Table C for the eighty ranks. 



II4 ADOLPHE QUETELET AS STATISTICIAN 

Scale of Possibility and Precision 



[556 









Scale of 


Scale of 


Scale of 




OUPS OF 


3 

O 


Possibility. 


Precision. 


Possibility. 


Gr 




Sum of the 








a 


Probability 


probabilities, 


Relative 








of drawing 


commencing 


probability 








each group — 


with most 


of drawing 








Table A. 


probable group 


each group 






1 




—Table B. 


— Table C. 


499 white and 500 black. 


.025225 


.025225 


1. 000000 


498 


501 " 


2 


.025124 


•G 50349 


.996008 


497 


502 " 


3 


.024924 


.075273 


.988072 


496 


503 " 


4 


.024627 


.O999OO 


.976285 


495 


504 " 


5 


.024236 


.124136 


.9607' 9 


494 


505 " 


6 


.023756 


.I47892 


.941764 


493 


506 " 


7 


.023193 


.171085 


.919429 


492 


507 " 


8 


.022552 


.193637 


.894040 


491 


508 " 


9 


.021842 


•215479 


.865882 


490 


509 " 


10 


.021069 


.236548 


.835261 


489 


510 " 


11 


.020243 


.256791 


.802506 


488 


511 " 


12 


.019372 


.276163 


.767956 


487 


512 " 


13 


.018464 


.294627 


.731058 


486 


513 " 


14 


.027528 


.312155 


,604860 


485 


514 " 


15 


.016573 


.338728 


,657008 


484 


515 " 


16 


.015608 


.344355 


X 18736 


483 


' 516 " 


17 


.014640 


.358975 


.580364 


482 


517 " 


18 


.013677 


.372652 


.542197 


481 


' 518 " 


19 


.012726 


.385378 


.504516 


480 


519 " 


20 


.011794 


.397172 


.467576 


479 


520 " 


21 


.010887 


.408060 


.431609 


478 


521 " 


22 


.010008 


.41807O 


.396815 



In deducing this scale Quetelet first found Table C. 1 
As already shown the number of chances of any com- 
bination is given by its coefficient in the binomial expan- 
sion. If one represents the probability of the most fre- 
quent combinations by unity, the relative probabilities of 
other combinations with respect to unity may be readily 



Ibid., " Addition," p. 274, et seq.; Letters, "Notes," p. 259, et seq. 



557] STATISTICAL METHOD n ^ 

found. Now the coefficient of the general term in the 
development of the binomial is 

m (m—i) (m — 2) . . . (m — n-\-i) 
1. 2. 3 ... ft 

and the term immediately following is 

tn (jn — 1) (m— 2) . . . (m — n-\-i) (m — n) 
1. 2. 3. . . n (» + i) 

These coefficients show the respective chances of two 

Tn — n 

succeeding- combinations. Their ratio is as 1 : — , 

fe n-\-i. 

If therefore the probability of the most frequent com- 
bination is represented by unity, the probability of the 

,. ' .. 1 • • ■, m — n 

immediately succeeding combination becomes — j_ — 

Moreover the coefficient of any term being known, the 

coefficient of the succeeding term may be found by 

m — n 
multiplying the known value by — ^r — It must be 

noted that n is always one less than the number of the 
known term. In drawing 999 balls at a time the most 
probable combination is 499 of one color and 500 of the 
other. This term in the series would be either the 500th 
or the 501st; as however Quetelet works with the second 
half of the symmetrical series, he begins with the 501st 
term. Representing its probability by unity, the prob- 
ability of the succeeding combination, that is, 498 white 

999 — 500 499 
and 501 black, becomes , i or ~~ This reduces 

to .996008. This is also the relative probability of draw- 
ing 498 black and 501 white. The probability of draw- 
ing 497 of one color and 502 of the other becomes 



H6 ADOLPHE QUETELET AS STATISTICIAN [558 

, m — n 499 498 

multiplied by -^q~f or —-- X - Q — By this process 

were found the successive values of Table C. 

Table A is next deduced. Designating by a, a ', a'\ 
etc., the successive values of Table C, and their sum by 
za, Quetelet states that the absolute probabilities of 

Table A result from the divisions indicated by — , — , 
,, ia la 

a 
— , etc. 1 Quetelet's description of his procedure is not 

z*a 

quite accurate at this point. The values of Table A are 

in fact found by the following divisions: , , , 

21a 22a 22a 

etc. The result of dividing each of the relative proba- 
bilities given in Table C by their sum is that the sum of 
the quotients thus obtained is equal to unity. This 
would mean that the sum of the absolute probabilities 
of one-half of the combinations should be considered 
equal to unity. But since the symbol of certainty is 
unity, the sum of the probabilities of one-half of the 
combinations must equal .50, as Table B indicates. 
Hence the individual relative probabilities must be 
divided by twice their sum in order to get the absolute 
probabilities. 

From Table A is found Table B by adding the suc- 
cessive values. The sum of the probabilities as given 
for eighty ranks in Table B, amounts to .4999992. 
Doubling this, so as to include the probabilities of the 
parallel groups, gives .9999984. As unity represents 
certainty, the difference between one and .9999984 or 
.0000016 represents the total probability of all combina- 
tions beyond 579 of one color and 420 of the other. 

^'Sur 1' appreciation, etc.,' 1 p. 275; Letters, pp. 260-261. 



559] STATISTICAL METHOD ny 

The distribution of the chances or probabilities for 
fifty combinations on each side of the most probable 
combinations is then presented graphically. 1 The re- 
spective probabilities are represented by rectangles, 
which by their relative sizes show the rapidity with 
which the probabilities diminish. Assuming that in 
nature the accidental causes of variation are infinite in 
number, and that consequently " events vary through 
infinite and imperceptible degrees," 2 it is necessary, in 
order accurately to represent nature, to conceive the 
number of rectangles to be indefinitely increased and 
their width indefinitely diminished, until the lines joining 
their tops merge into a continuous curve. This curve 
is the curve of possibilities (courbe des possibility). It 
shows the distribution of chances when their number is 
unlimited. Quetelet deduces the value of the mean term, 
or coefficient of the most probable combination when 
the number of terms is infinitely great, the probability of 
this term, and the formula for the curve of possibility 
itself. 3 He also makes a comparison between his scale, 
"calculated on the basis of a thousand different events," 
and that given by Cournot, " in which the probability of 
the expected event may pass through every possible 
gradation." He finds that one rank of his table corre- 
sponds closely to four and one-half ranks of Cournot's 
table. 4 

Throughout the foregoing development Quetelet con- 
tinually assumed that the chances were equally favorable 

x<< Sur l'appreciation, etc." § ix, and chart at end of that essay; 
Letters, p. 68. 
2 Ibid., p. 249. 

3 Ibid., p. 276, et seq.\ Letters, p. 263, et seq. 
"Ibid., p. 280, et seq.; Letters, p. 255, et seq. 



Il8 ADOLPHE QUETELET AS STATISTICIAN [560 

to white and black balls. On this assumption he gets, 
in theory, the perfectly symmetrical distribution of 
chances shown by the coefficients of the binominal ex- 
pansion. Moreover, this hypothesis provides for the 
occurrence of combinations farthest removed from the 
most probable one. Theoretically there is an infinites- 
imal probability for the combination having an infinite 
number of balls of one color. But, as Quetelet points 
out, 1 these extremely small probabilities may be ne- 
glected. When he comes to test the agreement between 
theory and practice 2 he finds that even in drawing as 
few as ten, eleven or twelve balls at a time, he does not 
get, in several hundred draws, a single combination of 
balls all of one color. Thus in experience the extreme 
combinations do not occur if the number of possible 
combinations is very great. 

Quetelet passes next to the application of his law of 
possibility to scientific observations. This application 
involves Quetelet's theory of means. He says, " the 
theory of Means serves as a basis to all sciences of obser- 
vation." 3 "In all things to which plus or minus may 
be applied, there are necessarily three things to consider, 
— one mean and two extremes." 4 "Means properly so 
called " are to be distinguished from " arithmetic means." 5 
Their difference was not in the process by which they are 
found, for both are found by the method of finding an 
arithmetic average, but rather in the nature of the obser- 
vations from which they are derived. The average of 
many measurements of the height of a certain house 
would give a true mean, while that of the heights of the 

l " Sur 1'appreciation, etc.," p. 243; Letters, pp. 66-67. 

*Ibid., §§ vi and vii; Letters, pp. 62, 254-255. 

% Letters, p. 38. K Ibid., p. 39. h Ibid., " Letter xi." 



g6l] STATISTICAL METHOD Iir) 

houses on a given street would be only an arithmetic 
mean. Many measurements of the same thing are bound 
together by a "law of continuity," I they are grouped 
about their average " in a determinate order, which is 
that assigned by the scale of possibility." 3 It was one 
of Quetelet's most important discoveries that the meas- 
urements of the height or other physical trait of a group 
of men were likewise grouped about their average. 
Thus the average height, as represented by the average 
man, is a true mean. 

Quetelet's law of the distribution of chances must first 
be related to the distribution of a set of measurements 
of the same thing about their mean and then to the dis- 
tribution of biological measurements. 3 We deal then 
first with the errors of the measurements. Quetelet did 
not define the term error. It may be defined (i) as the 
difference between the true value sought and any meas- 
urement or (2) as the difference between the average and 
any measurement. 4 As the average approaches the true 
value through more and more measurements, the two 
definitions finally coincide. Quetelet made no systematic 
statement of the hypotheses underlying the theory of the 
distribution of errors, but they may be found, expressly 
or impliedly, in his work. They may be stated as follows : 

(1) The average of a series of measurements repre- 

1 Letters, p. 42. 

2 Ibid., p. Jj; " Sur 1'appreciation, etc.," p. 250. 

8 Quetelet speaks indifferently of the distribution of errors and the 
distribution of measurements; and while of course the former distribu- 
tion determines the latter, it is to the distribution of errors that the dis- 
tribution of chances by the binominal law is assimilated. 

*See Mansfield Merriman, A Text-book on the Method of Least 
Squares (3rd ed., New York, 1888), p. 5. 



120 ADOLPHE QUETELET AS STATISTICIAN [$6 2 

sents an approximation to the true value sought. 1 
Theory indicates that the precision of this approxima- 
tion increases as the- square root of the number of obser- 
vations. 2 

(2) The causes of the errors are called accidental 
causes. They are very numerous, even infinite in num- 
ber; they act independently of each other; each is of 
small effect. 3 

(3) These causes are equally favorable to excess and 
to defect. " Each of the accidental causes . . . has the 
same probability of acting in one direction as (in) the 
other. This probability is then i-" 4 This is the same 
as the probability of drawing a white or a black ball from 
a bowl containing an equal number of balls of each color. 
For this reason the errors resulting from the various 
combinations of many accidental causes of error will be 
distributed according to the binomial law. From this it 
follows both that the errors are symmetrically distri- 
buted about the mean and that "small errors are more 
numerous than large ones," 5 or as Quetelet phrases it, 
the greater number of observations " occur in the im- 
mediate neighborhood" of the mean, and "the further 
we depart from the mean, the fewer observations will 
each group include." 6 

(4) Though the theory provides for errors of any 
amount, there are always more or less narrow limits 
beyond which errors do not occur. 

1 Letters, pp. 72, 76, 90. 

2 Ibid., p. 36, and " Letters" xvi and xvii. 

3 Ibid., pp. 22, 107, 108, et seq., passim. 

^Ibid., p. 280; see also pp. 77-78, 84. 

5 Merriman, op. cit., p. 15. 

6 Letters, pp. 77, go; "Sur l'appreciation, etc.," p. 250. 



563] STATISTICAL METHOD I2 i 

By very similar principles to the foregoing the law of 
the distribution of chances may be related to the distri- 
bution of biological measurements. In this case the 
average is an approximation to the group type. There 
are assumed to be a vast number of minute independent 
causes of deviation from the type or average, equally 
favorable to excess or deficiency of development. 
Finally small deviations are most numerous, the devia- 
tions become less numerous as they become larger, and 
there are limits beyond which deviations from the type 
do not occur in nature. Thus the Average Man becomes 
the type, about which all other men of a homogeneous 
group are distributed according to a definite law. 

It was in the foregoing manner that Quetelet trans- 
formed the law of the combinations of two independent 
events when the number of chances is very large, that is 
the binominal law, into a law of error, and then made 
this latter serve as the law of distribution of variations 
among living things. 

In testing the fit of a series of measurements to his 
scale of precision Quetelet usually made use of a table 
consisting of nine columns. 1 

The following example, showing the distribution of 
the chest measurements of 5738 Scotch soldiers, serves 
better than any other from Quetelet's writings to illus- 
trate the process involved : 

1 Sqq " Sur 1' appreciation, etc.," pp. 251, 252, 255, 259, 260; Letters, 
pp. 85, 88, 276, 277; and Bowley, Elements of Statistics (2d ed., Lon- 
don, 1902), pp. 278-279. 



122 



ADOLPHE QUETELET AS STATISTICIAN 



[564 





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1. 0000 


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The first column of this table gives the distribu- 
tion of the units of measurement, in this case inches. 
The second column gives the frequencies of each 
group. The third column presents a series of propor- 
tional numbers, or the proportion represented by each 
group frequency when their sum is made equal to unity, 
the symbol of certainty. The process followed is to 
divide the total number of observations into unity, and 
then to multiply this quotient by each frequency in turn. 
This column gives in fact the probabilities that a meas- 
urement will fall under the corresponding groups noted 
in column one. The distribution being assumed to be 
normal or symmetrical, one-half of the total number of 



565 J STATISTICAL METHOD I2 $ 

measurements, or .5000 of the total probabilities should 
be on either side of the mean. The fourth column 
shows the probability of not exceeding a given measure- 
ment, that is, the total probabilities of all measurements 
from and including the given measurement to the mean. 
It thus corresponds to Table B of the probability scale. 
It is found by working inward toward the mean from 
either extreme, subtracting from .5000 the successive 
probabilities given by column three. In the fifth column 
are given the ranks corresponding to the probabilities 
given in column four, Table B being used for this pur- 
pose. Column five thus gives the actual distribution of 
the observations in ranks of Quetelet's scale. 

In order to find the correspondence between experi- 
ence and theory the foregoing process is now reversed. 
From the actual distribution of column five a theoretical 
distribution is found, column six showing the ranks with 
a uniform difference between them. By this process the 
distribution is so " smoothed" that each group covers 
the same number of ranks. Quetelet does not show how 
he selected the common difference in smoothing the 
distribution, though it can be approximated by averag- 
ing the differences between the ranks as given in column 
five. There is doubtless an element of arbitrariness in 
the choice of this difference. The object being to find 
the difference which gives the closest fit of the curve to 
the measurements, the true value can be indefinitely ap- 
proached by repeated trials. From this sixth column is 
calculated, by the use of Table B, column seven corre- 
sponding to column four. The successive differences of 
column seven, working from the mean outward, give 
column eight, corresponding to column three. Column 
eight thus gives the probabilities that a measurement 
would fall under the respective groups, were they actu- 



124 ADOLPHE QUETELET AS STATISTICIAN [566 

ally to occur according to the assumptions of the prob- 
ability curve. In column nine appear the differences 
between the numbers of columns three and eight, show- 
ing the amount of the misfit for each group. 

But " each series of observations has its particular scale 
of possibility. . . . The nature of this scale is determined 
by the number of observations, as also by the more or 
less precise means employed in making such observa- 
tions." 1 If the observations are represented graphically 
by the curve of possibility, this curve contracts towards 
its axis in the ratio of the increase in the square root of 
the number of observations. 2 But assuming the observa- 
tions to be equally numerous, " the contraction towards 
the axis is proportional to the degree of precision of the 
observers, and gives a measure of that precision. Our 
aim then should be to seek means of appreciating the 
contraction of the curve." 3 Such a means is found in 
the probable error. As its name implies this is that 
error or deviation from the mean which is as often ex- 
ceeded as not exceeded. It thus designates the limits 
between which one-half of all the observations fall, or the 
divergence either side of the mean between which and 
the mean one-fourth of the observations are found. 4 
Since Table B of Quetelet's scale gives the sum of the 
probabilities on either side of the mean, it is only neces- 
sary to locate the value .2500 in this Table in order to 
determine the rank of the probable error. The precision 
for rank 10 is .236548, and for rank 11 it is . 256791. 5 
Interpolating, one gets 10.6645 as the rank of the prob- 
able error. 6 The number of ranks included between the 

1 Letters, p. 77. % Ibid., "Letter xvi." % Ibid., p. 80. 

4 " Sur l'appreciation, etc.," p. 257. 5 See p. 114, supra. 

6 Quetelet commonly speaks of this rank as "about 10.5;" "Sur 
l'appreciation, etc.," p. 257. In the Letters he gives the rank as 10.67 
on p. 271, and as "nearly 10.66" on p. 274. 



567] STATISTICAL METHOD I2 $ 

positive and negative limits of the probable error would 
therefore be twice 10.6645 or 2I -339°J Quetelet usually 
considered 21 ranks as sufficiently near the true value. 

Assuming that the distribution should be normal, 
Quetelet calculated the probable error from the smoothed 
data. Having determined the best uniform difference 
between the ranks as given in column six, 1 he divides 
this number into 21 and multiplies the quotient by the 
dimension of a group as given in column one. This 
gives him in concrete units the distance between the two 
limits of probable error. One-half of this distance gives 
the probable error. A comparison of the probable errors 
of two sets of measurements of the same thing he con- 
sidered a measure of their relative precision. 2 

In the notes of the Letters Quetelet calculates the odds 
of not exceeding 'various sizes of the probable error. 
This is done easily from Table B. Thus twice the prob- 
able error is 21.34 ranks. The precision for this rank is 
.411463, that is, .411463 out of .5000 of the probabilities 
lie between twice the probable error and the mean, while 
.500000 — .411463 or .088537 of them lie beyond this 
limit. The ratio of .411463 to .088537 is 4.64: 1. Simi- 
larly the odds in favor of three or more times the prob- 
able error may be calculated. 3 Quetelet also gives 4 the 
relation of the probable error to the standard deviation. 
He, however, does not seem to have made any use of 
the standard deviation, though he says it is a quantity 
"of great importance." 

It has been stated that Quetelet assumed the distribu- 

1 See p. 122, supra, 2 Letters, p. 82. 

5 Quetelet's method is somewhat more cumbrous though it gives sim- 
ilar results; Letters, p. 270, et seg. 
K Ibid., p. 272, et seg. 



I2 6 ADOLPHE QUETELET AS STATISTICIAN [568 

tion of the errors of a set of measurements to be sym- 
metrical. This same assumption, extended to the varia- 
tions in nature, gave a type about which the variations 
were evenly distributed. . Thus his mean in theory be- 
came not only an arithmetic average but also the median 
and the mode. 1 It was on this basis that Quetelet viewed 
the degree of misfit of the measurements to the scale of 
possibility as a test of the degree of accuracy with which 
the measurements were made. 2 It would seem to be 
quite as plausible to consider the degree of misfit as a 
test of the accuracy with which the assumptions under- 
lying the theoretical law of normal distribution can be 
applied to a particular set of observations. While we 
cannot, as the basis for a theory of the distribution, find 
any less arbitrary assumptions than that the causes of 
variation are infinite, minute and equal and that they are 
equally favorable to excess and deficiency, 3 yet it strains 
our credulity to believe that these assumptions must 
always be true to experience, especially in measurements 
of mass phenomena. In fact a perfect realization of 
these assumptions in experience would seem to be 
fortuitous, and deviations from the perfectly symmetrical 
distribution may vary through many degrees of asym- 
metry. The normal curve is thus to be viewed as a form 
of the distribution of variable objects in nature, approx- 
imately realized in some classes of phenomena, but as 
only one of the many possible forms. 

Of this Quetelet seems to have been quite aware. For 
while in his illustrations he always assumed the normal 

1 Bowley, op. tit., p. 119, apparently does not consider Quetelet' s 
average as the median and the mode. It is impossible to see how this 
conclusion can be reached. 

2 " Sur 1' appreciation, etc.," p. 272. 

3 See Jevons, op. tit., pp. 255 and 380. 



569] STATISTICAL METHOD 12 j 

distribution, he was fully aware of asymmetrical distri- 
bution and gave a satisfactory explanation of it. l He 
even contemplated part authorship of a treatment of 
such cases. 2 Quetelet explained the variations in nature 
not only by the various combinations of an infinite num- 
ber of independent and minute causes, but also by the 
different " degrees of intensity of which these causes are 
susceptible." 3 When therefore variations in one direc- 
tion are found to exceed those in the other, it is due to 
the causes operating in one direction having " much 
more probability than the contrary causes, either because 
they are more numerous or because they are more ener- 
getic." 4 When the observations are numerous, the 
skewness of their distribution becomes an indication of 
one or more causes more or less powerful, peculiarly 
favorable to variation in one direction. The normal dis- 
tribution being viewed as natural, skewness requires 
special explanation. 5 

It should be noted that while Quetelet gave very great 
importance to the determination of the average, and the 
probable deviation from the average, he also frequently 
emphasized the importance of changes in the limits of 
variation. His reason for this emphasis was his belief 
that " one of the principal effects of civilization is that it 
more and more contracts the limits within which the dif- 
ferent elements relating to man oscillate." 6 Believing 
the averages of human qualities to be for the most part 
stationary, he believed the perfectibility of man would be 

1 Some discussion of the unsymmetrical distribution as related to the 
theory of the Average Man was given on p. 81, et seg., supra. 

2 See Letters, p. 113. d Z6id., p. 106. 

i I5id., p. 124. 5 Bowley, op. cit., p. 267. 

*Sur Vhomme, closing section; English translation, pp. x and 108; 
Physique sociale, vol. ii, p. 428; Du Systeme social, p. 252, et seg. 



128 ADOLPHE QUETELET AS STATISTICIAN [570 

shown in an ever-increasing equality among men, physi- 
cally, intellectually and morally, until all approached the 
state of the Average Man. * His interpretation of the 
narrowing of the limits of variation was thus very differ- 
ent from the more recent view which finds in such nar- 
rowing an evidence of a more intense struggle for exist- 
ence, of more severe economic competition, 2 or of 
increased social pressure. 3 

Quetelet used the word " civilization " in the most gen- 
eral sense; its effects were shown in such phenomena as 
increased political equality, the prevention of famines and 
the general diffusion of a sufficiency of food, and the 
spread of knowledge through all classes. We may then 
note (1) that he centered attention upon the limits of 
variation from the type rather than upon the standard 
deviation of the group; it is the latter which shows best 
the massing of the group about the type, or the con- 
formity to the type; (2) that he did not give an inter- 
pretation of restricted variation in terms of biological or 
sociological causation, nor does his statement in any way 
suggest the process of natural selection or increased en- 
vironmental or social pressure as the explanation of the 
narrowed limits; and (3) from the sociological viewpoint 
social evolution (in order to avoid the term "civiliza- 
tion") seems to have resulted not only in an increased 
conformity of men to a type of individual capable of co- 
operation, but also in an increase of liberty, which im- 
plies greater freedom of variation. 4 The interpretation 

x For a discussion of Quetelet's confusion on this point see chap, iii, 
p. 72, et seq., supra. 

2 H. L. Moore, "The Variability of Wages," Political Science Quar- 
terly, March, 1907. 

3 F. H. Giddings, "The Measurement of Social Pressure," Quarterly 
Publications of the American Statistical Association, March, 1908. 

* Giddings, Sociology, a lecture delivered at Columbia University in 



571 ] STATISTICAL METHOD I2 g 

of a statistical fact which Quetelet readily found in " one 
of the effects of civilization," is thus seen to be, sociolog- 
ically, a difficult problem in balancing the effects of op- 
posing and complex processes and conditions. 

It remains to note Quetelet's classification of causes 
and his method of studying them. For besides making 
possible a more accurate description of social facts, 
Quetelet's principle of studying groups rather than in- 
dividuals opened the way for the study of the causal re- 
lation among mass phenomena. Having described a 
group by means of the average and an index of varia- 
bility, changes in these constants may be related to 
changes in the group conditions, that is, to causes suf- 
ficiently general to affect the whole or a large part of the 
group. The method itself thus suggests a classification 
of causes. 

As to their manner of action, Quetelet classified causes 
as constant, variable or accidental. I He says : 

Constant causes are those which act in a continuous man- 
ner, with the same intensity and in the same direction. Var- 
iable causes act in a continuous manner, with energies and 
tendencies which change. . . . Among variable causes it is 
above all important to distinguish such as are of a periodic 
character, as for instance the seasons. Accidental causes only 
manifest themselves fortuitously 2 and act indifferently in any 
direction/ 

the Series on Science, Philosophy and Art, February 26, 1908, p. 34, ei 
seg., especially pp. 39-40- 

1 Stir Vhomme, bk. iv, chap, ii; English translation, p. 103; " Sur 
l'appreciation, etc.," p. 207; Letters, p. 107. 

2 In Du Systeme social, pp. 305-306, he explains that he does not mean 
that any cause is really accidental. In using the term he merely follows 
established usage. The accidental causes are themselves necessary re- 
sults of their antecedents, but are called accidental because we cannot 
trace these antecedents. s Letters, p. 107. 



X^o ADOLPHE QUETELET AS STATISTICIAN [^ 2 

Among constant causes Quetelet named sex, age, pro- 
fession, season, latitude and economic and religious insti- 
tutions. In the first place it may be noted that Quetelet 
interpreted social phenomena in terms of external and 
purely formal conditions. To-day we are interested in 
sex, age,, profession as explanatory of social phenomena, 
only because of their implications with regard to human 
interests and mental traits. But it should not be over- 
looked that it is not possible to interpret social pheno- 
mena in terms of mental types until these types have 
been correlated with the external and formal conditions 
which Quetelet proposed. In the second place it may 
be doubted whether the above or any other causes are 
constant according to Quetelet's definition. He himself 
seems not to have been quite certain that really constant 
causes could be found. 1 Finally it should be recalled 
that Quetelet looked upon the average as the result of 
constant causes. It seems nearer the truth however to 
view the average as the final resultant of all causes, 
remembering that the more numerous the observations 
the more prominent become the effects of those causes 
which are most general in their influence. Since causes 
are appreciated through changes in the averages, per- 
fectly constant causes must remain inscrutable. Our 
nearest approach to such causes in statistical inquiry will 
be general causes which are relatively constant. 

Variable causes would seem to occupy a larger place 
in a satisfactory classification of causes than Quetelet 
gave them. Seasons appear in his discussion among 
both constant and variable causes. But if phenomena 
vary as we pass from one season to another, so do they 
as we pass from one age, sex, profession, or latitude to 

1 Letters, pp. 133, 144. 



273] STATISTICAL METHOD L ^ L 

another. It would seem in fact that all causes of social 
and organic phenomena, considered as mass phenomena, 
are more or less variable. Accepting the term then as a 
general characteristic of all such causes, we may find 
Quetelet's distinction of periodically variable causes 
highly useful. The seasons of the year and the hours of 
the day, or the revolution of the earth about the sun and 
its rotation on its axis, are of immense influence on 
organic life and in human affairs. 

The theoretical characterization of accidental causes 
has already been given. In measurements of social and 
organic phenomena they include two quite different sets 
of influences. These are first the causes of accidental 
errors in counting or measuring, as carelessness, lack of 
skill or variations in the precision of instruments, and 
secondly the many minute causes of variations in the 
phenomena themselves resulting in a more or less sym- 
metrical grouping about their average. Thus in ascer- 
taining the average height of a group of men, there 
would be mingled both the causes of errors of measure- 
ment and the causes of differences in the heights them- 
selves. That in both cases the causes are equal and act 
indifferently in favor of or in opposition to the average 
result is only a convenient hypothesis to be fulty justified 
in every case only by experience. But the point to be 
noted here is that the causes of variability though rela- 
tively "feeble" and "indirect," 1 are of varying degrees 
of feebleness and indirectness, depending upon the scope 
of the investigation. Thus in studying the heights of 
the men of a nation, the differences in race, age, place of 
habitation, nourishment, occupation would be merged 
together in the average. The group studied may how- 

1 Letters, p. 130. 



! 3 2 ADOLPHE QUETELET AS STATISTICIAN [574 

ever be steadily narrowed and each one of these condi- 
tions, which in the general study were deemed of minor 
importance, can be made most prominent. What is a 
minor cause for a wide group, becomes a general cause 
for a narrower group. There is of course a limit to this 
process of narrowing the group, for causes do not act 
singly, and with a very small group one condition can- 
not be sufficiently isolated — the number and variability of 
many small causes make the results too irregular. 

It would seem then that in any given group the causes 
influencing the observations range in extent from the 
very minute causes affecting individual cases only, 
through relatively minute causes to those general causes 
which affect most or all members of the group. It is 
only the latter which can produce a change in the 
average. These are the causes whose effects become 
more pronounced as the observations increase, the effects 
of all others being at the same time neutralized. We 
may thus classify all social causes as variable, and as 
either minute or general in their influence. 

Quetelet states that the art in the study of causes is to 
group the observations " in such a manner that all the 
causes, except those whose influence we wish to appreci- 
ate, may be considered as having acted equally on the 
members of each group." 1 If then differences in the 
results are found, they may be attributed to the influence 
studied. Thus he studied the relation of age, sex, 
season to the committing of crime by comparing the 
observations for one age, sex or season with those of 
another. This is in reality a study of causation through 
correlation or concomitant variation. With many meas- 
urements Quetelet held that accidental (or minor) causes 

1 Letters, p. 131. 



575] STATISTICAL METHOD ^3 

may be neglected, and the effects of constant (or gen- 
eral) causes will become prominent. The effects of peri- 
odic causes maybe studied by comparing parts of a period, 
as one season with another, and may be avoided by 
embracing an entire period, as a year. 1 From this 
simple and general basis given by Quetelet, the diffi- 
cult problem of studying causal relationships has been 
advanced to a method of quantitatively measuring the 
correlation of two variable elements throughout their 
distribution. 

"Letters, p. 141. 



BIBLIOGRAPHICAL NOTE. 

It does not seem necessary to give here a list of 
Quetelet's statistical publications, owing to the very 
thorough studies made by Georg Friedrich Knapp and 
published in Hildebrand's Jahrbilcher fur Nationalbkono- 
mie und Statistik, vol. xvii. Under the general title, 
" Bericht uber die Schriften Quetelets zur Socialstatistik 
und Anthropologic," Knapp gives first a classification of 
these writings both by form and by subject matter 
(p. 167, et seq.), secondly a statement of their contents, 
the writings being divided into three chronological 
periods (p. 342, et seq.) and thirdly a selection of the 
more important passages for the presentation of Quete- 
let's views on many topics (p. 427, et seq.). It is only 
necessary to refer the interested reader to these studies 
for bibliographical material. 

134 [576 



VITA 



The author of this dissertation was born in Willshire, 
Van Wert County, Ohio, September 27, 1877. After 
receiving the degree of A. B. from Baker University in 
1 90 1, he was principal of the public schools at Waverly, 
Kansas, for two years. He was enrolled as a graduate 
student under the Faculty of Political Science of 
Columbia University during the three years 1903-6 and 
during 1907-8. He was Scholar in Sociology 1904-5, 
and Fellow in Statistics 1905-6. During 1906-7 he was 
instructor in Economics and Sociology at Clark College, 
Worcester, Mass. While at Columbia he attended 
courses given by Professors Giddings, Clark, Seligman, 
Moore, Seager and Dunning. 

135 



LEMr'09 






^ 



k, 

ADOLPHE QUETELET 



* tf 



AS 



STATISTICIAN 



BY 

FRANK H. HANKINS, A. B. 

Sometime University Fellow in Statistics 



SUBMITTED IN PARTIAL FULFILMENT OF THE REQUIREMENTS 

FOR THE DEGREE OF DOCTOR OF PHILOSOPHY 

IN THE 

Faculty of Political Science 
Columbia University 



1908 

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